Browse Function problems Studdy Solved!

Problem 5901

The price of a certain object was $\$ 12.50$ in 1995 and $\$ 15.50$ in 2001. Assume that the price has been increasing at a constant rate since 1990.
Determine the rate of change in the price of the object, that is, how much the price increases each year. Do not round your answer. $\square$ Write an equation to model the price of the object over time, with $y$ representing the price of the object in dollars, and $x$ representing the number of years since 1990. Write your final answer in the form $y=m x+b$ . (You may use the point-slope form to help you find the equation.) $\square$ Looking at your equation, what was the price of the object in the year 1990? If necessary, round to your answer to two decimal places. \\square $How much does the object cost now, in 2024? \$$ \square$

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Problem 5902

(a) Determine if the upper bound theorem identifies 5 as an upper bound for the real zeros of $f(x)$ . (b) Determine if the lower bound theorem identifies -5 as a lower bound for the real zeros of $f(x)$ . $f(x)=x^{4}+14 x^{3}+x^{2}+4 x+39$

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Problem 5903

A car traveling on cruise control on an interstate highway passes mile marker 100, 1.5 hours after getting on the highway. Then, 2.5 hours after getting on the highway, the same car passes mile marker 160.
What is the car's constant speed? $\square$ miles per hour Write a linear equation modeling the car's travels, with $y$ representing the mile marker the car will have passed after $x$ hours on the highway. Write your final answer in $y=m x+b$ form. (You may start from the point-slope form to find your equation.) $\square$

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Problem 5904

$\sin ^{-1}(1.94)=$ $\square$ $\tan ^{-1}(2.27)=$ $\square$ $\cos ^{-1}(-0.62)=$ $\square$

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Problem 5905

Graphing rational functions with holes
Graph the rational function. $f(x)=\frac{3 x^{2}-15 x}{x^{2}-7 x+10}$
Start by drawing the asymptotes (if there are any). Then plot two points on each piece of the graph. Finally, click on the graph-a-function button. Be sure to plot a hollow dot wherever there is a "hole" in the graph.

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Problem 5906

\begin{align} &\text{Given the function:} \\ &y = 3 \sin 2(x-1) + 3 \end{align} $\text{Why is its ending point between } 2\pi \text{ and } \frac{5\pi}{2}? \text{ What is that value and how were we supposed to know it ends there?}$

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Problem 5907

$\begin{array}{c}\tan ^{-1}(-1.53)= \\ \cos ^{-1}(2.26)= \\ \sin ^{-1}(0.42)=\end{array}$

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Problem 5908

$\text{Show algebraically that } \lim_{t \rightarrow 0} \frac{dy}{dx} = 0 \text{ for } x(t) = 1 + 2\sin(t) \text{ and } y(t) = \ln(1 + \cos(t)) \text{ on } t \in (0, 2\pi).$

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Problem 5909

If $f(x)=\int_{4}^{x} t^{8} d t$ then $\begin{array}{l} f^{\prime}(x)= \\ f^{\prime}(4)= \end{array}$

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Problem 5910

A bacteria culture initially contains 1500 bacteria and doubles every half hour. Find the size of the bacterial population after 100 minutes. $\square$ Find the size of the bacterial population after 10 hours. $\square$

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Problem 5911

The half-life of caffeine in the human body is about 6.4 hours. A cup of coffee has about 100 mg of caffeine. a. Write an equation for the amount of caffeine in a person's body after drinking a cup of coffee? Let $C$ be the milligrams of caffeine in the body after $t$ hours. $\square$ b. How much caffeine will remain after 10 hours? $\square$ mg c. How long until there are only 20 mg remaining? $\square$ hours

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Problem 5912

5 Which of the following functions is not a linear function? (a) $y=-\frac{2}{3} x+\frac{11}{2}$ (b) $y=\frac{3-4 x}{7}$ c. $y=\frac{7}{3-4 x}$ d $y=3-x$

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Problem 5913

Find the zeros of $h(x)=5 x^{2}+40$ .
The zeros are $x=$ $\square$ and $x=$ $\square$ $\square$ .

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Problem 5914

Find the maximum rate of change of $f$ at the given point and the direction in which it occurs. $f(x, y)=\sin (x y), \quad(9,0)$
Step 1 Recall that the direction in which the maximum rate of change of $f(x, y)$ occurs at a point $(a, b)$ is given by the vector $\nabla f(a, b)$ . For $f(x, y)=\sin (x y)$ , we have $\nabla f(x, y)=\square$

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Problem 5915

b. Explain the meaning of the coordinates of the vertex for this model. Choose the correct explanation belo A. The ball reaches its maximum speed of 44.4 meters per second in 3 seconds. B. The ball reaches its maximum height of 49.6 meters in 2 seconds. C. The ball reaches its maximum height of 2 meters in 49.6 seconds. D. The ball hits the ground after 3 seconds at a speed of 44.4 meters per second.

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Problem 5916

Ex 9. Differentiate $m(x)=e^{x} f(x)$ $m^{\prime}(x)=$ $\qquad$
Ex 10. Differentiate $n(x)=\frac{f(x)}{e^{x}}$ $n^{\prime}(x)=$ $\qquad$
Ex 11. Differentiate $p(x)=\frac{\ln (x)}{f(x)}$ $p^{\prime}(x)=$ $\qquad$
Ex 12. Differentiate $q(x)=e^{f(x)}$ $q^{\prime}(x)=$ $\qquad$

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Problem 5917

Note: You have unlimited attempts on this question and it will not re-random a new version. This question is also worth 10 marks.
Please answer the following questions about the function $f(x)=\frac{3 x^{2}}{x^{2}-16}$
Instructions: - If you are asked for a function, enter a function. - If you are asked to find $x$ - or $y$ -values, enter either a number or a list of numbers separated by commas. If there are no solutions, enter None. - If you are asked to find intervals of increase/decrease/concavity, please separate the lists with commas and NOT the union symbol. - For the domain and range, use interval notation and NOT commas. - If you are asked to find a limit, enter DNE if the limit does not exist. (a) Calculate the first derivative of $f$ . Find the critical numbers of $f$ , where it is increasing and decreasing, and its local extrema. $f^{\prime}(x)=\frac{-96 x}{\left(x^{2}-16\right)^{2}}$
Critical numbers $x=$ $\square$ List of the intervals where $f(x)$ is increasing (separated by commas and NOT the union symbol) $(-\infty,-4),(-4,0)$ List of the intervals where $f(x)$ is decreasing (separated by commas and NOT the union symbol) $(0,4),(4, \infty)$ Local maxima $x=$ $\square$ Local minima $x=$ $\square$ (b) Find the following left- and right-hand limits at the vertical asymptote $x=-4$ . $\lim _{x \rightarrow-4^{-}} \frac{3 x^{2}}{x^{2}-16}=+ \text { infinity } \leqslant \quad \lim _{x \rightarrow-4^{+}} \frac{3 x^{2}}{x^{2}-16}=- \text { infinity }$
Find the following left- and right-hand limits at the vertical asymptote $x=4$ . $\lim _{x \rightarrow 4^{-}} \frac{3 x^{2}}{x^{2}-16}=- \text { Infinity } \rightarrow \quad \lim _{x \rightarrow 4^{+}} \frac{3 x^{2}}{x^{2}-16}=+ \text { infinity } \leqslant$
Find the following limits at infinity to determine any horizontal asymptotes. $\lim _{x \rightarrow-\infty} \frac{3 x^{2}}{x^{2}-16}=3$ (c) Calculate the second derivative of $f$ . Find where $f$ is concave up, concave down, and has inflection points. $f^{\prime \prime}(x)=\frac{96\left(3 x^{2}+16\right)}{\left(x^{2}-16\right)^{3}}$
List of the intervals where $f(x)$ is concave up (separated by commas and NOT the union symbol) $(-\infty,-4),(4, \infty)$ List of the intervals where $f(x)$ is concave down (separated by commas and NOT the union symbol) $(-4,4)$ Inflection points $x=$ None (d) The function $f$ is even $\leqslant$ because $f(-x)=f(x) \quad y$ for all $x$ in the domain of $f$ , and therefore its graph is symmetric about the $y$ -axis (e) Answer the following questions about the function $f$ and its graph.
The domain of $f$ is the set (in interval notation and NOT using commas) $(-\infty,-4) \cup(-4,4) \cup(4, \infty)$ The range of $f$ is the set (in interval notation and NOT using commas) 1 $y$ -intercept 0 $x$ -intercepts 0

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Problem 5918

Find the derivative of $f(x)=\frac{5 x^{4}-x^{2}-3}{x^{4}}$ . $f^{\prime}(x)=$ $\square$ Submit

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Problem 5919

Fill in the table using this function rule. $y=5 x-1$ \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline 1 & $\square$ \\ \hline 2 & $\square$ \\ \hline 5 & $\square$ \\ \hline 8 & $\square$ \\ \hline \end{tabular}

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Problem 5920

Given the function $f(x)=200(1.35)^{x}$ evaluate each of the following. Note: Round your answers to two decimal places as needed. \begin{tabular}{|l|c|} \hline A) Evaluate $f(-10)$ & $f(-10)=\square$ \\ \hline B) Evaluate $f(-5)$ & $f(-5)=\square$ \\ \hline C) Evaluate $f(0)$ & $f(0)=200$ \\ \hline D) Evaluate $f(5)$ & $f(5)=\square$ \\ \hline E) Evaluate $f(10)$ & $f(10)=\square$ \\ \hline \end{tabular}

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Problem 5921

WS: $30-2$ A6 Sem
7. The table below shows Canmore's population from 2010 to 2017. The data is taken from Alberta.ca Regional Dashboard. \begin{tabular}{|l|c|c|c|c|c|c|c|c|} \hline Year & 2010 & 2011 & 2012 & 2013 & 2014 & 2015 & 2016 & 2017 \\ \hline Population & 12841 & 12796 & 13177 & 13604 & 14037 & 14193 & 14646 & 14936 \\ \hline \end{tabular} a. Assuming the population of a Canmore has been growing exponentially, find the regression equation in the form $P(t)=a b^{t}$ , where $P(t)$ is the population and $t$ is the number of years since 2010 ( 2010 is year 0 in your calculator). Express the values of $a$ to the nearest whole number and $b$ to the nearest thousandth. (1 mark) b. Using your regression equation, calculate what the population of Canmore should have been, to the nearest whole number, in 2020. (1 mark) c. If the actual population of Canmore in 2020 was 14798 people, why might the predicted population be different than the actual population? ( 1 mark) d. Assuming that the growth rate of Canmore follows your regression equation, during what year will the population reach 18000 ? ( 1 mark)

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Problem 5922

c. (a) $\int x \sqrt{1-x} d x$

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Problem 5923

2. Given that $g(x)=\frac{1}{2} x+9$ and $h(x)=(x+1)(x-1)$ , determine the following. Simplify where possible. a. $h(x)-g(x)$ [1 mark] b. $h \times g(x)$ [2 marks] c. $\frac{h}{g}(x)$ [1 mark] d. $g \circ h(x)$ [2 marks] e. $h \circ g(x)$ [2 marks]

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Problem 5924

\begin{align} \text{Match the functions with their graphs.} \\
1. & \quad f(x) = \cos(x) \\
2. & \quad f(x) = \sin(x) \\
3. & \quad f(x) = \tan(x) \\
4. & \quad f(x) = \arcsin(x) \\
5. & \quad f(x) = \arccos(x) \\
6. & \quad f(x) = \arctan(x) \\ \text{Graphs:} \\ A & \\ B & \\ C & \\ D & \\ E & \\ F & \\ \end{align}

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Problem 5925

$\frac{1}{s^{2}+s-2}$ find partial fraction $\frac{s+1}{s^{2}+s-2}$ finde partial fraction

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Problem 5926

The function $h$ is defined below. $h(x)=\frac{x^{2}+3 x-40}{x^{2}-10 x+25}$
Find all values of $x$ that are NOT in the domain of $h$ . If there is more than one value, separate them with commas.

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Problem 5927

2. Diketahui fungsi $f(x)=5 x-2$ dan $g(x)=\frac{1}{x-2}, x \neq$ 2 tentukan komposisi fungsi $(g \circ f)(x)$ .

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Problem 5928

The displacement of a particle over time $t$ seconds is given by $x=2 e^{4 t} \mathrm{~m}$ . What is the initial displacement?

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Problem 5929

$g(x)=\frac{x-5}{(x-9)(x+8)}$ vertical asymptotes(s)
Select one: a. $x=9, x=-8$ b. $x=8, x=-9$ c. $x=-5$ d. $x=5$

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Problem 5930

14- the output current in the circuit contains dc source, L load with switch is closed at $t=0$ is a- Rise exponential b- Rise linearly c-Equal constant d-Rise linearly with forced component 15-The extinction angle of controlled rectifier with $r$ load circuit a-Sometimes equal zero degree b-Sometimes equal 180 degrees c-All times equal zero degree d-All times equal 180 degrees 16-If the maximum output voltage of r load circuit in the half-wave controlled rectifier with transformer supplied from Jordan electric city company is 63 v , the V 2 of transformer is $\mathrm{a}-140 \mathrm{v}$ b-63 v $\mathrm{c}-70 \mathrm{v}$ d-46.66 v 17 -the power of the load is 20000 watt with 220 v nominal voltage is connected with the single-phase source in Jordan with 16 ampere a-the source is damaged b-the load is worked well c-the load is damaged d-the load and the source are damaged 18 -If the van is reference of the three phase system so that the vab is a- leaded the van by 60 degree b-leaded the van by 30 degree c-lagged the van by 30 degree d-lagged the van by 60 degree 19 -the on-resistance is one of the semi- power devices parameters is selected with 3.-maximum ohm b-zero ohm c -minimum ohm d-infinity ohms 20-Forced component of re load in the circuit with ac source, diode and switch after is closed is a-( $\sqrt{2} \mathrm{~V} / \mathrm{Z}) \operatorname{Sin}\left(\mathrm{Cl}^{\mathrm{t}}-\theta\right)$ $\mathrm{b}-(\sqrt{2} \mathrm{Vm} / \mathrm{Z}) \operatorname{Sin}(\omega \mathrm{t}+\Theta)$ $c-(\sqrt{ } 2 \mathrm{~V} / \mathrm{r}) \operatorname{Sin}(\omega \mathrm{t}+\Theta)$ d- $(\sqrt{2} 2 \mathrm{~V} / \mathrm{Z}) \operatorname{Sin}\left(\omega^{2} t+\Theta\right)$ Question2: (10marks) Compare between the one pulse and two pulses controlled rectifier. Support your answer with curves, relations and circuit 3

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Problem 5931

Find the gradient of the tangent to the curve: a $y=x^{3}-3 x$ at the point where $x=5$

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Problem 5932

Explain the difference between an absolute minimum and a local minimum. A function $f$ has an absolute minimum at $x=c$ if $f(c)$ is the smallest function value on the entire domain of $f$ , whereas $f$ has a local $\mathbf{m}$ There is no difference. A function $f$ has an absolute minimum at $x=c$ if $f(c)$ is the largest function value on the entire domain of $f$ , whereas $f$ has a local min A function $f$ has an absolute minimum at $x=c$ if $f(c)$ is the smallest function value when $x$ is near $c$ , whereas $f$ has a local minimum A function $f$ has an absolute minimum at $x=c$ if $f(c$ is the largest function value when $x$ is near $c$ , whereas $f$ has a local minimum at

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Problem 5933

A. -2 B. 2 C. 0 D. $\infty$ E.None Q.33) Let $f(x)=2 x^{2}+3$ find the value of $x$ such that $f^{-1}(x)=2$ A. 19 B. 8 C. -19 D. 2 E.None

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Problem 5934

Sketch the graph of $f$ and use your sketch to find the absolute and local maximum and minimum values of $f$ . (Enter your answers as a comma-separate $f(x)=\ln (3 x), \quad 0<x \leq 5$ absolute maximum value $\square$ absolute minimum value $\square$ local maximum value(s) $\square$ local minimum value(s) $\square$

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Problem 5935

7. Find the interval where the graph of $f(x)=\frac{2 x}{4 x^{2}+1}$ is decreasing and increasing. Hence, determine the extremum points if exist.

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Problem 5936

Find any relative extrema of the function. (Round your ar $f(x)=\arctan (x)-\arctan (x-9)$ relative maximum $(x, y)=(4.5,2.702 x)$

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Problem 5937

The function $\frac{|x-2|}{x-2}$ has jump discontinuity at $x=2$ . Select one: True False IVR_TEAM

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Problem 5938

$\lim _{x \rightarrow 0^{+}} \sqrt{x} \cos \frac{\pi}{x}=$
Select one: a.
b. 1 c. DNE d. -1 e. 0

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Problem 5939

42. Find the domain of each function: (A) $f(x)=\frac{2 x-5}{x^{2}-x-6}$ (B) $g(x)=\frac{3 x}{\sqrt{5-x}}$
In Problems 57-59, find the equation of any horizontal asymptote.
57. $f(x)=\frac{5 x+4}{x^{2}-3 x+1}$
58. $f(x)=\frac{3 x^{2}+2 x-1}{4 x^{2}-5 x+3}$
53. Explain how the graph of $m(x)=-|x-4|$ is related to the graph of $y=|x|$ .
54. Explain how the graph of $g(x)=0.3 x^{3}+3$ is related to the graph of $y=x^{3}$ .
19. Complete the square and find the standard form for the quadratic function $f(x)=-x^{2}+4 x$
Then write a brief verbal description of the relationship between the graph of $f$ and the graph of $y=x^{2}$ .

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Problem 5940

F24 HW9 70\% mathmatize.com
Question \#6: No response Score: --
The following table gives values of the differentiable function $y=f(x)$ . \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|} \hline $x$ & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \hline $y$ & 3 & 5 & 4 & -2 & 1 & 2 & 1 & -2 & -3 & -4 & -7 \\ \hline \end{tabular}
Estimate the $x$ -values of critical points of $f(x)$ on the interval $0<x<10$ . Classify each critical point as a local maximum, local minimum, or neither.
Critical points (in ascending order) and its classifications are as follows: (1) the critical point is at $x=$ $\square$ and it is $\square$ (2) the critical point is at $x=$ $\square$ and it is $\square$ (3) the critical point is at $x=$ $\square$ and it is $\square$ Now assume that the table gives values of the continuous function $y=f^{\prime}(x)$ (instead of $f(x)$ ). Estimate and classify critical points of the function $f(x)$ .
Critical points (in ascending order) and its classifications are as follows: (1) the critical point is at $x=$ $\square$ and it is $\square$ (2) the critical point is at $x=$ $\square$ and it is $\square$ (3) the critical point is at $x=$ $\square$ and it is $\square$

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Problem 5941

On considère la fonction numérique $f$ définie sur $\mathbb{R}^{+}$ par : $f(x)=x(\sqrt{x}-2)^{2}$
Et soit $\left(C_{f}\right)$ sa courbe représentative dans un repère orthonormé $(O ; \vec{i} ; \vec{j})$ 1) Calculer : $\lim _{x \rightarrow+\infty} f(x) \text { et } \lim _{x \rightarrow+\infty} \frac{f(x)}{x}$
Que peut-on déduire ? 2)Etudier la dérivabilité de la fonction $f$ à droite en 0 puis interpréter le résultat obtenu. 3) a-Montrer que pour tout $x \in] 0 ;+\infty[$ : $f^{\prime}(x)=2(\sqrt{x}-1)(\sqrt{x}-2)$ b-Etudier le signe de $f^{\prime}(x)$ puis dresser le tableau de variations de la fonction $f$ . 4) Etudier la concavité de la courbe ( $C_{f}$ ) et Montrer que $\left(C_{f}\right)$ Admet un unique point d'inflexion I auquel on déterminera ses coordonnées. 5) Résoudre dans $\mathbb{R}^{+}$ l'équation $f(x)=x$ et interpréter le résultat graphiquement. 6) Tracer la courbe $\left(c_{f}\right)$ dans le repère ( $(i ; \vec{i} ; \vec{j})$ . 7) Soit $g$ la restriction de la fonction $f$ sur $\boldsymbol{I}=[\mathbf{4} ;+\infty[$ . a-Montrer que $g$ admet une fonction réciproque $g^{-1}$ définie sur un intervalle $J$ à déterminer. b-Dresser le tableau de variations de la fonction $g^{-1}$ . c-Calculer $g(9)$ puis déterminer $\left(g^{-1}\right)^{\prime}(9)$ d -Montrer que pour tout $x \in J$ : $g^{-1}(x)=(\sqrt{1+\sqrt{x}}+1)^{2}$ 8) Tracer la courbe $\left(C_{g^{-1}}\right)$ dans le repère $(O ; \vec{i} ; \vec{\jmath})$ .

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Problem 5942

Find the indicated derivative. $\begin{array}{c} y=(h x+k)^{6}, y^{\prime \prime \prime} \\ y^{\prime \prime \prime}=\square \end{array}$

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Problem 5943

$\lim _{x \rightarrow \infty} \frac{3 x(x-7)}{x+7}$

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Problem 5944

Lines Finding slope given the graph of a line in quadrant 1 that models a real-...
Keisha makes house calls. For each, she is paid a base amount and makes additional money for each hour she works. The graph below. shows her pay (i dollars) versus the number of hours worked.
Use the graph to answer the questions. (a) How much does her pay increase for each hour worked? \\square$ (h) What is the slone of the line?

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Problem 5945

Uort J la fonction définie sur l'intervalle $] 0 ;+\infty\left[\right.$ par $f(x)=x-(\ln (x))^{2}$ Et soit ( $C$ ) sa couribe représentative dans un repère orthonormé $(0, i, j)$ (unité
1- Montrer que l'axe des ordonnés est une asymptote à la courbe ( $C$ ) 2-: $a$ - Montrer que $\lim _{x \rightarrow+\infty} f(x)=+\infty$ et que la courbe (C) admet parabolique de direction la droite ( $\Delta$ ) d'équation $y=x$ au voisinage de

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Problem 5946

Exi : 1) Etudier la dérivabilité en $x_{0}$ des fonctione sulvantes : $f(x)=\frac{x-3}{x^{2}+3}, x_{0}=1 ; g(x)=\sqrt{x} ; x_{0}=1$

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Problem 5947

22. Let $X$ denote the proportion of allotted time that a randomly selected student spends working on a certain aptitude test. Suppose the pdf of $X$ is $f(x, \theta)=\left\{\begin{array}{cl} (\theta+1) x^{\theta} & 0 \leq x \leq 1 \\ 0 & \text { otherwise } \end{array}\right.$ where $-1<\theta$ . A random sample of ten students yields data $x_{1}=.92, x_{2}=.79, x_{3}=.90, x_{4}=.65$ , $x_{5}=.86, x_{6}=.47, x_{7}=.73, x_{8}=.97, x_{9}=.94$ , $x_{10}=.77$ . a. Use the method of moments to obtain an estimator of $\theta$ and then compute the estimate for this data. b. Obtain the maximum likelihood estimator of $\theta$ and then compute the estimate for the given data.

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Problem 5948

Question Video Examples
Given $h(x)=-4 x-3$ , find $h(2)$ .
Answer Attempt 1 out of 2 $\square$ Submit Answer

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Problem 5949

Find the terms through degree 4 of the Maclaurin series of $f$ . Use multiplication and substitution as necessary. $f(x)=(1+x)^{-5 / 3}$

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Problem 5950

For the following function, find the full power series centered at $x=0$ and then give the first 5 nonzero terms of the power series and the open interval of convergence. $\begin{array}{l} f(x)=\sum_{n=0}^{\infty} f(x)=\frac{x^{3}}{(1+8 x)^{2}} \\ f(x)=x^{3}+-16 x^{4}+192 x^{5}+-2048 x^{6}+20480 x^{7}+\cdots \end{array}$
The open interval of convergence is: $\left(-\frac{1}{8}, \frac{1}{8}\right)$ (Give your answer in interval notation.).

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Problem 5951

6. Advertisers try to measure the Click-Through Rate (CTR) for their ads, which gives the 3.5 ratio of people who click on an ad (Total Clicks on Ad) compared to the people who see the ad (Total Impressions), For example, a CTR of 0.05 means that $5 \%$ of the people seeing the ad actually click on the ad and follow the link. A company initiates a new marketing strategy in the hope of increasing their CTR score. Let $C(t)$ represent the company's CTR, $t$ weeks into the initlative. What are the units of $C^{\prime}(t)$ ? \begin{tabular}{|c|c|c|c|} \hline clicks & $\frac{\text { clicks }}{\text { week }}$ & $\frac{\text { clicks/impression }}{\text { week }}$ & $\frac{\text { clicks }}{\text { impression }^{2}}$ \\ Red & Blue & Ught green & Orange \\ \hline \end{tabular}

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Problem 5952

Find the value of $f(-3)$ .
Answer Attempt 1 out of 2 $\square$ Submit Answer

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Problem 5953

Odredite drugu derivaciju funkcije $f(x)=-4 x \cdot 3^{x}$ u točki $x_{0}=3$ .
Odgovor: $f^{\prime \prime}(3)=$ $\square$ . Napomena: Ako odgovor nije cijeli broj, zaokružite ga na dvije decimale (npr. 1.23).

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Problem 5954

The equation of an exponential function has the form $y=A b^{x}$ . How can you tell from the equation whether the exponential function represents growth or decay?

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Problem 5955

Express the function graphed on the axes below as a piecewise function.
Answer Altempt 1 put of 3 $f(x)=\left\{\begin{array}{ll}\square & \text { for } \square \\ \square & \text { for } \square\end{array}\right.$ $\square$ $\square$ $\square$ $\square$ $\square$ Adi Rule Remowe Rule Submit Answer

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Problem 5956

Use the graph of the function f shown to the right to find $f(1), f(2)$ , and f(3). $f(1)=$ $\square$ $f(2)=$ $\square$ $f(3)=$ $\square$

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Problem 5957

NATIONAL 5 MATHS 2014 126
10. The graph of $y=a \sin (x+b)^{\circ}, 0 \leq x \leq 360$ , is shown below.
Write down the values of $a$ and $b$ .

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Problem 5958

Q.13) If $f(x)=\frac{\sec x}{x+3}$ and $\mathrm{f}^{-1}(\mathrm{c})=0$ , then $\mathrm{c}=$ A. $\frac{1}{3}$ B. 0 C. $\frac{2}{\sqrt{3}}$ D. $\frac{1}{4}$ E.None

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Problem 5959

NATIONAL 5 MATHS 2014 126
10. The graph of $y=a \sin (x+b)^{\circ}, 0 \leq x \leq 360$ , is shown below.
Write down the values of $a$ and $b$ .

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Problem 5960

For the given function, use your intuition or additional research, if necessary, to complete parts (a) through (c) below. (angle of football, horizontal distance traveled by football) a. Describe an appropriate domain and range for the function. b. Make a rough sketch of a graph of the function. c. Briefly discuss the validity of the graph as a model of the true function. a. Choose the appropriate domain for the function below. A. The domain is the horizontal distances traveled by the football thrown at certain angles or 0 ft to 200 mi . B. The domain is all angles a football could be thrown at or $0^{\circ}$ to $360^{\circ}$ . C. The domain is all angles a football could be thrown at or $0^{\circ}$ to $90^{\circ}$ . D. The domain is the horizontal distances traveled by the football thrown at certain angles or 0 ft to 200 ft .

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Problem 5961

Using the substitution: $u=x^{9}-2$ . Re-write the indefinite integral then evaluate in terms of $u$ . $\int 10 x^{8}\left(x^{9}-2\right)^{10} d x=\int u^{10} \frac{10}{9} d u=\frac{10}{99} u^{11}+c$

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Problem 5962

Identify the vertex, and the $y$ -intercept then graph $f(x)=x^{2}-4 x+2$ . Hint: Click the vertex, then click another point of the parabola (like the $y$ -intercept). The vertex is ( $\square$ $\square$ The $y$ -intercept is ( 0 , $\square$ )

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Problem 5963

Given $g(x)=x^{4}+\frac{2}{x}$ , find $g^{\prime}(x)$ . $g^{\prime}(x)=$ $\square$ help (formulas).

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Problem 5964

a) Bestimmen Sie die Gleichungen der Tangenten an den Graphen der natürlichen Exponentialfunktion in den Punkten $\mathrm{A}(1 \mid \mathrm{e})$ und $\mathrm{B}\left(-1 \mid \mathrm{e}^{-1}\right)$ .

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Problem 5965

- • علامة
السؤال الثالث ا- بكم طريقة يمكن اختيار لجنة مكونة من 5 طلاب من صف يحوي على $ا$ طلاب؟
بـ اذا كان احتمال ان ينجح احمد في الاحصاء P(A)=0.6 واحتمال ان ينجح في الحاسوب P(B)=0.8 واحتمال ان ينجح في المقررين معا 0.48 اجب عما يلي 1 ـ مـا احتمال ان لا ينجح في أي من المقررين r - ما احتمال ان ينجح في الاحصاء ولا ينجح في الحاسوب

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Problem 5966

3 A thermocouple consists of two junctions between two metals; when one junction is at a higher temperature than the other, an emf is generated.
The hot junction and the cold junction of a thermocouple are at 373 K and 273 K , respectively. The emf generated is 1.0 mV . Show that the emf changes to 0.85 mV when the hot junction is moved to a water bath at 358 K , if the emf generated varies linearly with the temperature difference between the junctions.

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Problem 5967

Q.42) The range of the function $f(x)=2 \sec x$ equals A. R B. $R-[-2,2]$ C. R-(-2,2) D. $(-2,2)$

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Problem 5968

B) Verify that the function $f(x)=x^{2}-2 x+8$ satisfies the hypotheses of Rolle's Theorem on the interval $[-1,3]$ . Then find all numbers $c$ that satisfy the conclusion of Rolle's Theorem.

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Problem 5969

Quanto Griffin HW Units 9.2 Question 9, 9.2.29 HW Score: 27\%, 5.4 of 20 points Points: 0 of 1 Save list
Use the horizontal line test to determine whether the function is one-to-one. $f(x)=\frac{8}{x^{2}-5}$
Is the function one-to-one? Yes No $\begin{array}{l} {[-10,10,-10,10] X \mathrm{Xcl}=1} \\ \mathrm{Yscl}=1 \end{array}$

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Problem 5970

At least one of the answers above is NOT correct.
Find the global maximum value of $f(x)=x^{3}-12.6 x^{2}+47.6 x-52.8$ on the interval $[-1,5.2]$ . The global maximum occurs at $x=$ $\square$ , and the maximum value is $y=$ $\square$ .

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Problem 5971

Determine the base function using easy methods for the exponential growth function:
$y = 104100(1.02)^{(x-1960)}$

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Problem 5972

Find the inverse for each of the following functions. $\begin{array}{l} f(x)=15 x+12 \\ f^{-1}(x)=\square \\ g(x)=6 x^{3}-3 \\ g^{-1}(x)= \\ h(x)=\frac{15}{x+3} \\ h^{-1}(x)=\square \\ j(x)=\sqrt[3]{x+6} \\ j^{-1}(x)=\square \end{array}$ $\square$ $\square$ $\square$ $\square$

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Problem 5973

Approximate $\int_{2}^{14} x^{2} d x$ using each of the following Riemann sums with 4 subintervals of equal length. Do not simplify your answer. (a) Left Riemann Sum = $\square$ (b) Right Riemann Sum = $\square$ (c) Midpoint Rule $=$ $\square$

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Problem 5974

Math 110 Course Resources - Definite Integrals Course Packet on the Fundamental Theorem of Calculus
Use the Fundamental Theorem of Calculus to evaluate the following definite integral. $\int_{2}^{7} 7 x-28 d x=$ $\square$ Submit Answer 2. [-/1 Points] DETAILS MY NOTES
Math 110 Course Resources - Definite Integrals Course Packet on the Fundamental Theorem of Calculus
Evaluate $\int_{-3}^{3} e^{3 x}+6 x^{2}-3 d x$ $\square$

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Problem 5975

$f(x)=\sinh \left(\log _{2} x\right)$ , then $f^{\prime}(x)=$ A) $\cosh \left(\log _{2} x.\right)$ B) $\cosh ($

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Problem 5976

Given $f(x)=-3 x^{2}+x-7$ and $g(x)=5 x+11$ , find: a) $(f+g)(x)$ $-3 x^{2}+6 x+4$ 06 b) the domain, in interval notation, of $(f+g)(x)$ $(-\infty, \infty) \curvearrowright \sigma^{4}$ c) $(f-g)(x)$ $-3 x^{2}-4 x-18$ d) the domain, in interval notation, of $(f-g)(x)$ $(-\infty, \infty) \sqrt{6}$ e) $(f-g)(x)$ $-15 x^{3}-28 x^{2}-24 x-77 \quad \sigma^{6}$ f) the domain, in interval notation, of ( $\mathrm{f} \cdot \mathrm{g})(\mathrm{x})$ $(-\infty, \infty) \curvearrowright 0^{6}$

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Problem 5977

6 Gegeben sind die Funktionen $f$ und $g$ mit $f(x)=e^{x}$ und $g(x)=e^{-x}$ und die Punkte $A(1 \mid f(1))$ und $\mathrm{B}(1 \mid \mathrm{g}(1)$ ). a) Zeigen Sie, dass sich die beiden Graphen orthogonal schneiden. b) Bestimmen Sie die Gleichungen der Tangenten an die jeweiligen Graphen in den Punkten A und B. Unter welchem Winkel schneiden sich die Tangenten? c) Bestimmen Sie den Schnittwinkel der Tangente an den Graphen von fim Punkt A(u|f(u)) mit der Tangente an den Graphen von g im Punkt $\mathrm{B}(\mathrm{u} \mid \mathrm{g}(\mathrm{u}))$ .

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Problem 5978

The string shown in the figure is driven at a frequency of 5.00 Hz . The amplitude of the motion is $A=11.5 \mathrm{~cm}$ , and the wave speed is $v=22.5 \mathrm{~m} / \mathrm{s}$ . Furthermore, the wave is such that $y=0$ at $x=0$ and $t=0$ . (i) (a) Determine the angular frequency for this wave (in rad/s). $\square$ rad/s (b) Determine the wave number for this wave (in rad/m). $\square$ $\mathrm{rad} / \mathrm{m}$ (c) Write an expression for the wave function. (Use the following as necessary: $t, x$ . Let $x$ be in meters and $t$ be in seconds. not include units in your answer. Assume SI units.) $y=\square \sin (\square)$ (d) Calculate the maximum transverse speed (in $\mathrm{m} / \mathrm{s}$ ). $\square$ $\mathrm{m} / \mathrm{s}$ (e) Calculate the maximum transverse acceleration of an element of the string (in $\mathrm{m} / \mathrm{s}^{2}$ ). $\square$ $\mathrm{m} / \mathrm{s}^{2}$ (f) What If? If the driving frequency is now doubled to 10.0 Hz , what are the maximum transverse speed (in $\mathrm{m} / \mathrm{s}$ ) and maximum transverse acceleration (in $\mathrm{m} / \mathrm{s}^{2}$ ) of an element of the string? maximum transverse speed $\square$ $\mathrm{m} / \mathrm{s}$ maximum transverse acceleration $\square$ $\mathrm{m} / \mathrm{s}^{2}$

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Problem 5979

Question 1 of 10, Step 1 of 2 0/14 Correct 3
A company makes two grades of paint, grade I, guaranteed for 5 years, and grade II, guaranteed for 10 years. A gallon of grade I costs $\$ 3.50$ to make, while a gallon of grade II costs $\$ 3.70$ to make. The weekly fixed costs are $\$ 3450$ .
Step 1 of 2 : Find the cost function $C(x, y)$ for making $x$ gallons of grade I and $y$ gallons of grade II. Answer Tables Keypad Keyboard Shortcuts $C(x, y)=\square$ Submit Answer

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Problem 5980

The function $f$ is shown below. If $g$ is the function defined by $g(x)=\int_{3}^{x} f(t) d t$ , find the value of $g^{\prime \prime}(3)$ in simplest form.

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Problem 5981

2. Find the derivative of the function using the limit definition of derivative. (c) $f(x)=\frac{1}{x^{2}-4}$

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Problem 5982

Question 9 of 10, Step 1 of 1 9/14 Correct 0
A company manufactures two models of a product, model $\boldsymbol{A}$ and model $\boldsymbol{B}$ . The cost for model $\boldsymbol{A}$ is $\$ 39$ and the cost for model $\boldsymbol{B}$ is $\$ 21$ . If the fixed costs are $\$ 640$ , the total cost function is given by $C(x, y)=640+39 x+21 y$ , where $x$ is the number of model $A$ and $y$ is the number of model $B$ . Find $C(56,60)$ . Answer Tables Keypad Keyboard Shortcuts $C(56,60)=\$ \square$ Submit Answer

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Problem 5983

Soit $f(x)=\frac{x+1}{x-1}$ tel que $x \neq 1$ alors $f^{\prime}(3)=$ a) $\frac{1}{2}$ b) 0 c) $-\frac{1}{2}$

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Problem 5984

s 2.2, Question 4, 2.2.13 Part 1 of 5 HW Score: $10 \%, 3$ of 30 points Points: 0 of 1 Save
Given the function $h$ described by $h(x)=x+16$ , firid each of the following. $h(0)=$

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Problem 5985

$\begin{array}{l}\int\left(\sec ^{2} x+7\right) d x \\ \int\left(\sec ^{2} x+7\right) d x=\square\end{array}$

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Problem 5986

(a) What is Kala's pay for a house call if she doesn't work any hours $\$ \square$ (b) What is her pay if she works 1 hour? $\$ 5$

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Problem 5987

For the following function $f$ , find the antiderivative $F$ that satisfies the given condition. $f(u)=5 e^{u}-19 ; F(0)=-2$
The antiderivative that satisfies the given condition is $F(u)=$ $\square$

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Problem 5988

Use a calculator to graph the function and estimate the value of the limit, then use L'Hôpital's rule to find the limit directly. $\lim _{x \rightarrow 0^{+}} \frac{\ln (x)}{\sin (x)}$
DNE

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Problem 5989

A retail store estimates that weekly sales $s$ and weekly advertising costs $\boldsymbol{x}$ (both in dollars) are related by $s=50000-390000 e^{-0.0008 x}$
The current weekly advertising costs are 2000 dollars and these costs are increasing at the rate of 300 dollars per week. Find the current rate of change of sales.
Rate of change of sales $=$ $\square$

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Problem 5990

Heights $(\mathrm{cm})$ and weights $(\mathrm{kg})$ are measured for 100 randomly selected adult males, and range from heights of 133 to 193 cm and weights of 41 to 150 kg . Let the predictor variable $x$ be the first variable given. The 100 paired measurements yield $\bar{x}=167.34 \mathrm{~cm}, \bar{y}=81.41 \mathrm{~kg}, \mathrm{r}=0.193, P$ -value $=0.054$ , and $\hat{y}=-106+1.11 x$ . Find the best predicted value of $\hat{y}$ (weight) given an adult male who is 184 cm tall. Use a 0.01 significance level.
Click the icon to view the critical values of the Pearson correlation coefficient r .
The best predicted value of $\hat{y}$ for an adult male who is 184 cm tall is 81.41 kg . (Round to two decimal places as needed.)

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Problem 5991

$\int_{1}^{\sqrt{7}} \frac{8}{1+x^{2}} d x$

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Problem 5992

3. Find the derivatives of the following (a) $g(x)=4 x+7$ (b) $F(t)=t^{3}+e^{3}$

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Problem 5993

the inverse of a mapping $f$ exists if $f$ is الإجابة a. onto mapping b. one to one mapping c. fixed mapping d. one to one and onto mapping

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Problem 5994

Use the following table to estimate $\int_{0}^{25} f(x) d x$ . Assume that $f(x)$ is a decreasing function. \begin{tabular}{c|c|c|c|c|c|c} \hline $x$ & 0 & 5 & 10 & 15 & 20 & 25 \\ \hline $f(x)$ & 49 & 47 & 44 & 37 & 27 & 7 \\ \hline \end{tabular}
To estimate the value of the integral we use the left-hand sum approximation with $\Delta x=$ $\square$
Then the left-hand sum approximation is $\square$
To estimate the value of the integral we can also use the right-hand sum approximation with $\Delta x=$ $\square$ Then the right-hand sum approximation is $\square$
The $\square$ of the left-and right sum approximations is a better estimate which is $\square$

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Problem 5995

What is $\lim _{x \rightarrow \infty} \frac{2^{t}+7}{5^{t}+9}$ ? That is what is the long run behavior?

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Problem 5996

Which of the following are true?
1. If velocity is constant and positive, then distance traveled during a time interval is the velocity multiplied by the length of the interval.
2. If velocity is positive and increasing, using the velocity at the beginning of each subinterval in a rectangle sum gives an overestimate of the distance traveled. Just 2 Both 1 and 2 Just 1 Neither 1 or 2 Clear my selection

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Problem 5997

Question 2 (1 point) A car starts from rest and continues at a rate of $v=\frac{1}{8} t^{2} \mathrm{ft} / \mathrm{s}$ . Find the function that relates the distance $s$ the car has traveled to the time $t$ in seconds.

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Problem 5998

Part 1 of 2
Use the graph of $f(x)$ to find the $x$ -intercepts of the graph and the zeros of the function.
The $x$ -intercepts are $\square$ (Type ordered pairs. Use a comma to separate answers.)

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Problem 5999

ALEKS - 2024 Fall - College Alga A ALEKS-Alden Scott-Knowled www-awa.aleks.com/alekscgi//x/lsl.exe/10_u-lgNsIkr7j8P3jH-IQgKSJS_J3Lykq19bMqn3Sx1kuBwVjDD2XFImfpifl. C. K12 Bookmarks 品 Mall - Scott, Aiden E. Sioux Falls SD 49-5 e-hallpass Dashboard Knowledge C Question 3 Aiden
The credit remaining on a phone card (in dollars) is a linear function of the total calling time made with the card (in minutes). The remaining credit after 34 Españot minutes of calls is $\$ 25.24$ , and the remaining credit after 58 minutes of calls is $\$ 21.88$ . What is the remaining credit after 76 minutes of calls? s! $\square$ $\times$ 5 IDon't Know SNopmit

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Problem 6000

a) Determine $\csc \theta, \sec \theta$ and $\cot \theta$ b) Calculate $\theta$ to the nearest degrees.

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Function

Problem 5901

Problem 5902

(a) Determine if the upper bound theorem identifies 5 as an upper bound for the real zeros of f(x)f(x)f(x). (b) Determine if the lower bound theorem identifies -5 as a lower bound for the real zeros of f(x)f(x)f(x). f(x)=x4+14x3+x2+4x+39f(x)=x^{4}+14 x^{3}+x^{2}+4 x+39f(x)=x4+14x3+x2+4x+39

Problem 5903

Problem 5904

sin⁡−1(1.94)=\sin ^{-1}(1.94)=sin−1(1.94)= □\square□ tan⁡−1(2.27)=\tan ^{-1}(2.27)=tan−1(2.27)= □\square□ cos⁡−1(−0.62)=\cos ^{-1}(-0.62)=cos−1(−0.62)= □\square□

Problem 5905

Problem 5906

Problem 5907

tan⁡−1(−1.53)=cos⁡−1(2.26)=sin⁡−1(0.42)=\begin{array}{c}\tan ^{-1}(-1.53)= \\ \cos ^{-1}(2.26)= \\ \sin ^{-1}(0.42)=\end{array}tan−1(−1.53)=cos−1(2.26)=sin−1(0.42)=​

Problem 5908

Problem 5909

If f(x)=∫4xt8dtf(x)=\int_{4}^{x} t^{8} d tf(x)=∫4x​t8dt then f′(x)=f′(4)=\begin{array}{l} f^{\prime}(x)= \\ f^{\prime}(4)= \end{array}f′(x)=f′(4)=​

Problem 5910

A bacteria culture initially contains 1500 bacteria and doubles every half hour. Find the size of the bacterial population after 100 minutes. □\square□ Find the size of the bacterial population after 10 hours. □\square□

Problem 5911

Problem 5912

5 Which of the following functions is not a linear function? (a) y=−23x+112y=-\frac{2}{3} x+\frac{11}{2}y=−32​x+211​ (b) y=3−4x7y=\frac{3-4 x}{7}y=73−4x​ c. y=73−4xy=\frac{7}{3-4 x}y=3−4x7​ d y=3−xy=3-xy=3−x

Problem 5913

Find the zeros of h(x)=5x2+40h(x)=5 x^{2}+40h(x)=5x2+40.The zeros are x=x=x= □\square□ and x=x=x= □\square□ □\square□.

Problem 5914

Problem 5915

Problem 5916

Problem 5917

Problem 5918

Find the derivative of f(x)=5x4−x2−3x4f(x)=\frac{5 x^{4}-x^{2}-3}{x^{4}}f(x)=x45x4−x2−3​. f′(x)=f^{\prime}(x)=f′(x)= □\square□ Submit

Problem 5919

Fill in the table using this function rule. y=5x−1y=5 x-1y=5x−1 \begin{tabular}{|c|c|} \hlinexxx & yyy \\ \hline 1 & □\square□ \\ \hline 2 & □\square□ \\ \hline 5 & □\square□ \\ \hline 8 & □\square□ \\ \hline \end{tabular}

Problem 5920

Problem 5921

Problem 5922

c. (a) ∫x1−xdx\int x \sqrt{1-x} d x∫x1−x​dx

Problem 5923

Problem 5924

Problem 5925

1s2+s−2\frac{1}{s^{2}+s-2}s2+s−21​ find partial fraction s+1s2+s−2\frac{s+1}{s^{2}+s-2}s2+s−2s+1​ finde partial fraction

Problem 5926

The function hhh is defined below. h(x)=x2+3x−40x2−10x+25h(x)=\frac{x^{2}+3 x-40}{x^{2}-10 x+25}h(x)=x2−10x+25x2+3x−40​Find all values of xxx that are NOT in the domain of hhh. If there is more than one value, separate them with commas.

Problem 5927

2. Diketahui fungsi f(x)=5x−2f(x)=5 x-2f(x)=5x−2 dan g(x)=1x−2,x≠g(x)=\frac{1}{x-2}, x \neqg(x)=x−21​,x= 2 tentukan komposisi fungsi (g∘f)(x)(g \circ f)(x)(g∘f)(x).

Problem 5928

The displacement of a particle over time ttt seconds is given by x=2e4t mx=2 e^{4 t} \mathrm{~m}x=2e4t m. What is the initial displacement?

Problem 5929

g(x)=x−5(x−9)(x+8)g(x)=\frac{x-5}{(x-9)(x+8)}g(x)=(x−9)(x+8)x−5​ vertical asymptotes(s)Select one: a. x=9,x=−8x=9, x=-8x=9,x=−8 b. x=8,x=−9x=8, x=-9x=8,x=−9 c. x=−5x=-5x=−5 d. x=5x=5x=5

Problem 5930

Problem 5931

Find the gradient of the tangent to the curve: a y=x3−3xy=x^{3}-3 xy=x3−3x at the point where x=5x=5x=5

Problem 5932

Problem 5933

A. -2 B. 2 C. 0 D. ∞\infty∞ E.None Q.33) Let f(x)=2x2+3f(x)=2 x^{2}+3f(x)=2x2+3 find the value of xxx such that f−1(x)=2f^{-1}(x)=2f−1(x)=2 A. 19 B. 8 C. -19 D. 2 E.None

Problem 5934

Problem 5935

7. Find the interval where the graph of f(x)=2x4x2+1f(x)=\frac{2 x}{4 x^{2}+1}f(x)=4x2+12x​ is decreasing and increasing. Hence, determine the extremum points if exist.

Problem 5936

Find any relative extrema of the function. (Round your ar f(x)=arctan⁡(x)−arctan⁡(x−9)f(x)=\arctan (x)-\arctan (x-9)f(x)=arctan(x)−arctan(x−9) relative maximum (x,y)=(4.5,2.702x)(x, y)=(4.5,2.702 x)(x,y)=(4.5,2.702x)

Problem 5937

The function ∣x−2∣x−2\frac{|x-2|}{x-2}x−2∣x−2∣​ has jump discontinuity at x=2x=2x=2. Select one: True False IVR_TEAM

Problem 5938

lim⁡x→0+xcos⁡πx=\lim _{x \rightarrow 0^{+}} \sqrt{x} \cos \frac{\pi}{x}=x→0+lim​x​cosxπ​=Select one: a.b. 1 c. DNE d. -1 e. 0

Problem 5939

Problem 5940

Problem 5941

Problem 5942

Find the indicated derivative. y=(hx+k)6,y′′′y′′′=□\begin{array}{c} y=(h x+k)^{6}, y^{\prime \prime \prime} \\ y^{\prime \prime \prime}=\square \end{array}y=(hx+k)6,y′′′y′′′=□​

Problem 5943

lim⁡x→∞3x(x−7)x+7\lim _{x \rightarrow \infty} \frac{3 x(x-7)}{x+7}limx→∞​x+73x(x−7)​

Problem 5944

Problem 5945

Problem 5946

Exi : 1) Etudier la dérivabilité en x0x_{0}x0​ des fonctione sulvantes : f(x)=x−3x2+3,x0=1;g(x)=x;x0=1f(x)=\frac{x-3}{x^{2}+3}, x_{0}=1 ; g(x)=\sqrt{x} ; x_{0}=1f(x)=x2+3x−3​,x0​=1;g(x)=x​;x0​=1

Problem 5947

Problem 5948

Question Video ExamplesGiven h(x)=−4x−3h(x)=-4 x-3h(x)=−4x−3, find h(2)h(2)h(2).Answer Attempt 1 out of 2 □\square□ Submit Answer

Problem 5949

Find the terms through degree 4 of the Maclaurin series of fff. Use multiplication and substitution as necessary. f(x)=(1+x)−5/3f(x)=(1+x)^{-5 / 3}f(x)=(1+x)−5/3

Problem 5950

Problem 5951

Problem 5952

Find the value of f(−3)f(-3)f(−3).Answer Attempt 1 out of 2 □\square□ Submit Answer

(a) Determine if the upper bound theorem identifies 5 as an upper bound for the real zeros of $f(x)$ . (b) Determine if the lower bound theorem identifies -5 as a lower bound for the real zeros of $f(x)$ . $f(x)=x^{4}+14 x^{3}+x^{2}+4 x+39$

$\sin ^{-1}(1.94)=$ $\square$ $\tan ^{-1}(2.27)=$ $\square$ $\cos ^{-1}(-0.62)=$ $\square$

$\begin{array}{c}\tan ^{-1}(-1.53)= \\ \cos ^{-1}(2.26)= \\ \sin ^{-1}(0.42)=\end{array}$

If $f(x)=\int_{4}^{x} t^{8} d t$ then $\begin{array}{l} f^{\prime}(x)= \\ f^{\prime}(4)= \end{array}$

A bacteria culture initially contains 1500 bacteria and doubles every half hour. Find the size of the bacterial population after 100 minutes. $\square$ Find the size of the bacterial population after 10 hours. $\square$

5 Which of the following functions is not a linear function? (a) $y=-\frac{2}{3} x+\frac{11}{2}$ (b) $y=\frac{3-4 x}{7}$ c. $y=\frac{7}{3-4 x}$ d $y=3-x$

Find the zeros of $h(x)=5 x^{2}+40$ .
The zeros are $x=$ $\square$ and $x=$ $\square$ $\square$ .

Find the derivative of $f(x)=\frac{5 x^{4}-x^{2}-3}{x^{4}}$ . $f^{\prime}(x)=$ $\square$ Submit

Fill in the table using this function rule. $y=5 x-1$ \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline 1 & $\square$ \\ \hline 2 & $\square$ \\ \hline 5 & $\square$ \\ \hline 8 & $\square$ \\ \hline \end{tabular}

c. (a) $\int x \sqrt{1-x} d x$

$\frac{1}{s^{2}+s-2}$ find partial fraction $\frac{s+1}{s^{2}+s-2}$ finde partial fraction

The function $h$ is defined below. $h(x)=\frac{x^{2}+3 x-40}{x^{2}-10 x+25}$
Find all values of $x$ that are NOT in the domain of $h$ . If there is more than one value, separate them with commas.

2. Diketahui fungsi $f(x)=5 x-2$ dan $g(x)=\frac{1}{x-2}, x \neq$ 2 tentukan komposisi fungsi $(g \circ f)(x)$ .

The displacement of a particle over time $t$ seconds is given by $x=2 e^{4 t} \mathrm{~m}$ . What is the initial displacement?

$g(x)=\frac{x-5}{(x-9)(x+8)}$ vertical asymptotes(s)
Select one: a. $x=9, x=-8$ b. $x=8, x=-9$ c. $x=-5$ d. $x=5$

Find the gradient of the tangent to the curve: a $y=x^{3}-3 x$ at the point where $x=5$

A. -2 B. 2 C. 0 D. $\infty$ E.None Q.33) Let $f(x)=2 x^{2}+3$ find the value of $x$ such that $f^{-1}(x)=2$ A. 19 B. 8 C. -19 D. 2 E.None

7. Find the interval where the graph of $f(x)=\frac{2 x}{4 x^{2}+1}$ is decreasing and increasing. Hence, determine the extremum points if exist.

Find any relative extrema of the function. (Round your ar $f(x)=\arctan (x)-\arctan (x-9)$ relative maximum $(x, y)=(4.5,2.702 x)$

The function $\frac{|x-2|}{x-2}$ has jump discontinuity at $x=2$ . Select one: True False IVR_TEAM

$\lim _{x \rightarrow 0^{+}} \sqrt{x} \cos \frac{\pi}{x}=$
Select one: a.
b. 1 c. DNE d. -1 e. 0

Find the indicated derivative. $\begin{array}{c} y=(h x+k)^{6}, y^{\prime \prime \prime} \\ y^{\prime \prime \prime}=\square \end{array}$

$\lim _{x \rightarrow \infty} \frac{3 x(x-7)}{x+7}$

Exi : 1) Etudier la dérivabilité en $x_{0}$ des fonctione sulvantes : $f(x)=\frac{x-3}{x^{2}+3}, x_{0}=1 ; g(x)=\sqrt{x} ; x_{0}=1$

Question Video Examples
Given $h(x)=-4 x-3$ , find $h(2)$ .
Answer Attempt 1 out of 2 $\square$ Submit Answer

Find the terms through degree 4 of the Maclaurin series of $f$ . Use multiplication and substitution as necessary. $f(x)=(1+x)^{-5 / 3}$

Find the value of $f(-3)$ .
Answer Attempt 1 out of 2 $\square$ Submit Answer

Odredite drugu derivaciju funkcije $f(x)=-4 x \cdot 3^{x}$ u točki $x_{0}=3$ .
Odgovor: $f^{\prime \prime}(3)=$ $\square$ . Napomena: Ako odgovor nije cijeli broj, zaokružite ga na dvije decimale (npr. 1.23).

The equation of an exponential function has the form $y=A b^{x}$ . How can you tell from the equation whether the exponential function represents growth or decay?

Use the graph of the function f shown to the right to find $f(1), f(2)$ , and f(3). $f(1)=$ $\square$ $f(2)=$ $\square$ $f(3)=$ $\square$

NATIONAL 5 MATHS 2014 126
10. The graph of $y=a \sin (x+b)^{\circ}, 0 \leq x \leq 360$ , is shown below.
Write down the values of $a$ and $b$ .

Q.13) If $f(x)=\frac{\sec x}{x+3}$ and $\mathrm{f}^{-1}(\mathrm{c})=0$ , then $\mathrm{c}=$ A. $\frac{1}{3}$ B. 0 C. $\frac{2}{\sqrt{3}}$ D. $\frac{1}{4}$ E.None

NATIONAL 5 MATHS 2014 126
10. The graph of $y=a \sin (x+b)^{\circ}, 0 \leq x \leq 360$ , is shown below.
Write down the values of $a$ and $b$ .

Using the substitution: $u=x^{9}-2$ . Re-write the indefinite integral then evaluate in terms of $u$ . $\int 10 x^{8}\left(x^{9}-2\right)^{10} d x=\int u^{10} \frac{10}{9} d u=\frac{10}{99} u^{11}+c$

Identify the vertex, and the $y$ -intercept then graph $f(x)=x^{2}-4 x+2$ . Hint: Click the vertex, then click another point of the parabola (like the $y$ -intercept). The vertex is ( $\square$ $\square$ The $y$ -intercept is ( 0 , $\square$ )

Given $g(x)=x^{4}+\frac{2}{x}$ , find $g^{\prime}(x)$ . $g^{\prime}(x)=$ $\square$ help (formulas).

a) Bestimmen Sie die Gleichungen der Tangenten an den Graphen der natürlichen Exponentialfunktion in den Punkten $\mathrm{A}(1 \mid \mathrm{e})$ und $\mathrm{B}\left(-1 \mid \mathrm{e}^{-1}\right)$ .

Q.42) The range of the function $f(x)=2 \sec x$ equals A. R B. $R-[-2,2]$ C. R-(-2,2) D. $(-2,2)$

B) Verify that the function $f(x)=x^{2}-2 x+8$ satisfies the hypotheses of Rolle's Theorem on the interval $[-1,3]$ . Then find all numbers $c$ that satisfy the conclusion of Rolle's Theorem.

Determine the base function using easy methods for the exponential growth function:
$y = 104100(1.02)^{(x-1960)}$

Approximate $\int_{2}^{14} x^{2} d x$ using each of the following Riemann sums with 4 subintervals of equal length. Do not simplify your answer. (a) Left Riemann Sum = $\square$ (b) Right Riemann Sum = $\square$ (c) Midpoint Rule $=$ $\square$