Browse Calculus problems Studdy Solved!

Problem 501

Given the function $f(x)=-3 \sin \left(\sqrt{4+3 x^{3}}\right)$ , find $f^{\prime}(x)$ .
Answer Attempt 1 out of 2 $f^{\prime}(x)=$ Subnuit Answer

See Solution

Problem 502

Given the function $h(x)=\frac{\sqrt{1-6 x^{3}}}{\sin ^{2}(x)}$ , find $h^{\prime}(x)$ in any form. Note: make sure to write trig functions using parentheses like $\sin ^{2}(x)$ instead of $\sin ^{2} x$ , otherwise expression.
Answer Attempt i out of 2 $h^{\prime}(x)=$ $\square$ Submit Answer

See Solution

Problem 503

25 Dans chaque cas, $f$ est une fonction définie et dérivable sur un intervalle I de courbe représentative $C_{f}$ dans un repère. Déterminer une équation de la tangente T à $C_{f}$ au point d'abscisse $a$ .
1. $f(x)=x^{3}$ et $a=-2$
3. $f(x)=\sqrt{x}$ et $a=2$
2. $f(x)=\frac{1}{x}$ et $a=-1$
Pour les exercices 26 à 30 Soit $f$ une fonction définie sur un ensemble I . Préciser son ensemble de dérivabilité $\mathrm{D}_{f^{\prime}}$ et déterminer sa dérivée $f^{\prime}$ .
26 1. $f(x)=x^{3}+x^{2} ; \mathrm{I}=\mathbb{R}$
2. $f(x)=x^{3}-x^{2}-x-1 ; I=\mathbb{R}$
3. $f(x)=\sqrt{x}+x ; \mathrm{I}=[0 ;+\infty[$
4. $f(x)=x^{2}-\frac{1}{x} ; I=\mathbb{R}^{*}$
27. 1. $f(x)=3 x^{2}-4 x+3 ; \mathrm{I}=\mathbb{R}$
2. $f(x)=-4 x^{4}+3 x^{3}-2 x^{2}+x ; \mathrm{I}=\mathbb{R}$
3. $f(x)=x^{3}-2 x^{2}+3 x-4 ; I=\mathbb{R}$

See Solution

Problem 504

1. $x^{3} y+x y^{3}=-8 x y$

See Solution

Problem 505

50 [chercher.]
On donne $\mathrm{I}=\left[-2 ; \frac{1}{2}\right]$ et $a=0$ . Sachant que T passe par A et par le point $\mathrm{B}\left(\frac{1}{2} ; 2\right)$ , calculer $f^{\prime}(a)$ .

See Solution

Problem 506

Car $A$ is traveling westat $80 \mathrm{~km} / \mathrm{h}$ and car B is traveling north at $100 \mathrm{~km} / \mathrm{h}$ . Both are headed for the intersection of the roads. At what rate are the cars approaching each other when car $A$ is 0.3 km and car B is 0.4 km from the intersection? Solution: Animation: Figure 3.9.004.

See Solution

Problem 507

Question Watch Video Show Examples
Given the function $f(x)=-\frac{5 \sqrt{x}}{2}-\frac{\sqrt{x^{3}}}{3}$ , find $f^{\prime}(4)$ . Express your answer as a single fraction in simplest form.
Answer Attempt 1 out of 10 $f^{\prime}(4)=$ $\square$ Submit Answer $\sqrt{ }$ $\sqrt[n]{ }$

See Solution

Problem 508

Question Watch Video Show
Given the function $f(x)=\left(-6+2 x^{-3}\right)\left(x^{2}+8 x^{-1}+10\right)$ , fin in any form.
Answer Attempt 1 out of 10 $f^{\prime}(x)=$ $\square$ Submit

See Solution

Problem 509

Consider the function $f(x)=7-|x|$ defined on $[-7,7]$ . (a) Compute the left Riemann sum $L_{5}$ . $L_{5}=$ $\square$ help (numbers) (b) Compute the right Riemann sum $R_{5}$ . $R_{5}=$ $\square$ help (numbers) (c) Compute the average value of $L_{5}$ and $R_{5}$ .
Average value $=$ $\square$ help (numbers) (d) Compute the area under the graph of f .
Area $=$ $\square$ help (numbers) (e) Compare the two values found in (c) and (d).
The average value is $\square$ the area.

See Solution

Problem 510

(a) Find the Riemann sum for $f(x)=x-2 \sin (2 x), 0 \leq x \leq 3$ , with six terms, taking the sample points to be right endpoints. Give your answer correct to six decimal points. $R_{6}=$ (b) Repeat (a) with midpoints as the sample points. $M_{6}=$

See Solution

Problem 511

Given the function $f(x)=\cos (\pi x)$ , compute the right-endpoint (Riemann) sum using $n=3$ on the interval $[0,1]$ . $R_{3}=$ help (numbers)

See Solution

Problem 512

In this problem you will calculate the area between $f(x)=6 x^{3}$ and the $x$ -axis over the interval $[0,2]$ using a limit of right-endpoint Riemann sums: $\text { Area }=\lim _{n \rightarrow \infty}\left(\sum_{k=1}^{n} f\left(x_{k}\right) \Delta x\right)$
Express the following quantities in terms of $n$ , the number of rectangles in the Riemann sum, and $k$ , the index for the rectangles in the Riemann sum. a. We start by subdividing $[0,2]$ into $n$ equal width subintervals $\left[x_{0}, x_{1}\right],\left[x_{1}, x_{2}\right], \ldots,\left[x_{n-1}, x_{n}\right]$ each of width $\Delta x$ . Express the width of each subinterval $\Delta x$ in terms of the number of subintervals $n$ . $\Delta x=\square$ b. Find the right endpoints $x_{1}, x_{2}, x_{3}$ of the first, second, and third subintervals $\left[x_{0}, x_{1}\right],\left[x_{1}, x_{2}\right],\left[x_{2}, x_{3}\right]$ and express your answers in terms of $n$ . $x_{1}, x_{2}, x_{3}=\square \text { (Enter a comma separated list.) }$ c. Find a general expression for the right endpoint $x_{k}$ of the $k$ th subinterval $\left[x_{k-1}, x_{k}\right\}$ , where $1 \leq k \leq n$ . Express your answer in terms of $k$ and $n$ . $x_{k}=$ $\square$ d. Find $f\left(x_{k}\right)$ in terms of $k$ and $n$ . $f\left(x_{k}\right)=$ $\square$ e. Find $f\left(x_{k}\right) \Delta x$ in terms of $k$ and $n$ . $f\left(x_{k}\right) \Delta x=$ $\square$ f. Find the value of the right-endpoint Riemann sum in terms of $n$ . $\sum_{k=1}^{n} f\left(x_{k}\right) \Delta x=$ $\square$ g. Find the limit of the right-endpoint Riemann sum. $\lim _{n \rightarrow \infty}\left(\sum_{k=1}^{n} f\left(x_{k}\right) \Delta x\right)=$ $\square$

See Solution

Problem 513

Find the function $f(x)$ described by the given initial value problem. $\begin{array}{l} f^{\prime \prime}(x)=2 \sin x, \quad f^{\prime}(\pi)=2, \quad f(\pi)=4 \\ f(x)=\square \end{array}$

See Solution

Problem 514

Consider the function $f(x)$ whose second derivative is $f^{\prime \prime}(x)=5 x+8 \sin (x)$ . If $f(0)=4$ and $f^{\prime}(0)=4$ , what is $f(x)$ ? $f(x)=$

See Solution

Problem 515

Find $L^{-1}\left\{\frac{-3}{s-2}+\frac{4}{(s-2)^{2}}+\frac{7}{s+5}\right\}$

See Solution

Problem 516

Find $L^{-1}\left\{\frac{1}{s^{8}}+\frac{1}{s^{5}}+\frac{1}{s^{2}}\right\}$

See Solution

Problem 517

Find the general indefinite integral. Use an upper-case $C$ for any arbitrary constants. $\int 7 z^{-3}+4 z^{-2}+3 z^{-1} d z=$ $\square$

See Solution

Problem 518

Find the general indefinite integral. Use an upper-case $C$ for any arbitrary constants. $\int(6-t)\left(-7+t^{2}\right) d t=$ $\square$

See Solution

Problem 519

Find $L^{-1}\left\{\frac{1}{s^{2}+2 s+37}\right\}$

See Solution

Problem 520

Find the general indefinite integral. Use an upper-case $C$ for any arbitrary constants. $\int\left(x^{5}+5+\frac{5}{x^{2}+1}\right) d x=$ $\square$

See Solution

Problem 521

Find the most general antiderivative of the function $g(u)=5 u^{5}-3 u^{2}-6$ . Use an upper-case $C$ for any arbitrary constants. $G(u)=$

See Solution

Problem 522

Find $f$ if $f^{\prime}(x)=-5+9 x$ and $f(0)=2$ . $f(x)=$

See Solution

Problem 523

$F(x)=$

See Solution

Problem 524

[0/7 Points] DETAILS MY NOTES
Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) $g(x)=\sqrt[3]{16-x^{2}}$

See Solution

Problem 525

Find $\lim _{x \rightarrow 3} \frac{x^{2}-x-6}{x-3}$

See Solution

Problem 526

Example 6: (self-study) Find the abs. max and abs. $\min$ values of $f$ on the given interval $f(x)=x^{3}-3 x^{2}+1, \quad\left[-\frac{1}{2}, 4\right]$ Solution:

See Solution

Problem 527

Find the most general antiderivative of the function $f(t)=-4 \cos (t)-10 \sin (t)$ . Use an upper-case $C$ for any arbitrary constants. $F(t)=$

See Solution

Problem 528

Find $\lim _{x \rightarrow 0^{+}}(\cot x)^{x}$

See Solution

Problem 529

Find the family of antiderivatives of the function $\begin{array}{l} f(x)=\frac{8.5}{\sqrt{x^{7}}} \\ F(x)= \end{array}$

See Solution

Problem 530

Consider the function $f(x)=\frac{7}{x^{4}}-\frac{8}{x^{6}}$ . Let $F(x)$ be the antiderivative of $f(x)$ with $F(1)=0$ . Compute $F(2)$ . $F(2)=$ $\square$ Submit answer Next item wers Attempt 2 of 2

See Solution

Problem 531

Math 2211 Classwork over 4.1 and 4.3
1. (10 points) Consider $f(x)=x^{4}-6 x^{2}$ . (a) Find the critical numbers of the function. (b) Find the intervals on which $f$ is increasing or decreasing. (c) Find the local maximum and minimum values of $f$ . (d) Find the inflection points. (e) Find the intervals of concavity.

See Solution

Problem 532

Find $f$ . $f(x)=\square$

See Solution

Problem 533

Differentiate implicitly to find $\frac{d^{2} y}{d x^{2}}$ . $\begin{array}{l} 3 x^{3}-y^{3}=5 \\ \frac{d^{2} y}{d x^{2}}=\square \end{array}$

See Solution

Problem 534

For the demand function $q=D(p)=367-p$ , find the following. a) The elasticity b) The elasticity at $\mathrm{p}=111$ , stating whether the demand is elastic, inelastic or has unit elasticity c) The value(s) of $p$ for which total revenue is a maximum (assume that $p$ is in dollars) a) Find the equation for elasticity. $E(p)=$ $\square$ b) Find the elasticity at the given price, stating whether the demand is elastic, inelastic or has unit elasticity. $E(111)=$ $\square$ (Simplify your answer. Type an integer or a fraction.)
Is the demand elastic, inelastic, or does it have unit elasticity? elastic inelastic unit elasticity c) Find the value(s) of $p$ for which total revenue is a maximum (assume that $p$ is in dollars). $\$$ $\square$

See Solution

Problem 535

Differentiate implicitly to find $\frac{d y}{d x}$ . Then find the slope of the curve at the given point. $\begin{array}{l} 2 x^{2}+3 x y+6 y^{2}+13 y-8=0 ; \quad(-2,0) \\ \frac{d y}{d x}=\square \end{array}$ $\square$

See Solution

Problem 536

(1 point) a. Find the Laplace transform $F(s)=\mathcal{L}\{f(t)\}$ of the function $f(t)=9+\sin (8 t)$ , defined on the interval $t \geq 0$ . $F(s)=\mathcal{L}\{9+\sin (8 t)\}=$ $\square$ help (formulas) b. For what values of $s$ does the Laplace transform exist? $\square$ help (inequalities)
Note: You can earn partial credit on this problem.

See Solution

Problem 537

Standard 16: Problem 4 (1 point) a. Find the Laplace transform $F(s)=\mathcal{L}\{f(t)\}$ of the function $f(t)=2 e^{-9 t}+3 t+6 e^{10 t}$ , defined on the interval $t \geq 0$ . $F(s)=\mathcal{L}\left\{2 e^{-9 t}+3 t+6 e^{10 t}\right\}=$ $\square$ help (formulas) b. For what values of $s$ does the Laplace transform exist? $\square$ help (inequalities)
Note: You can earn partial credit on this problem.

See Solution

Problem 538

A garden shop determines the demand function $q=D(x)=\frac{4 x+300}{10 x+11}$ during early summer for tomato plants where $q$ is the number of plants sold per day when the price is $x$ dollars per plant. (a) Find the elasticity. (b) Find the elasticity when $x=2$ . (c) At $\$ 2$ per plant, will a small increase in price cause the total revenue to increase or decrease? (a) The elasticity is $\square$ (b) When $x=2$ , the elasticity is $\square$ (Simplify your answer. Type an integer or a fraction) (c) Fill in the blank below.
At $\$ 2$ per plant, a small increase in price will cause the total revenue to $\square$

See Solution

Problem 539

(1 point) a. Set up an integral for finding the Laplace transform of the following function: $f(t)=\left\{\begin{array}{ll} 0, & 0 \leq t<6 \\ t-3, & 6 \leq t . \end{array}\right.$ $F(s)=\mathcal{L}\{f(t)\}=\int_{A}^{B} \square$ help (formulas) where $A=$ $\square$ and $B=$ $\square$ b. Find the antiderivative (with constant term 0 ) corresponding to the previous part. $\square$ c. Evaluate appropriate limits to compute the Laplace transform of $f(t)$ : $F(s)=\mathcal{L}\{f(t)\}=$ $\square$ d. Where does the Laplace transform you found exist? In other words, what is the domain of $F(s)$ ? $\square$ help (inequalities)

See Solution

Problem 540

Previous Problem Problem List Next Problem
Standard 16: Problem 6 (1 point)
Find the Laplace transform of $5 \cos (a t)-2 e^{m t}$ : $\square$
Preview My Answers Submit Answers You have attempted this problem 0 times. You have unlimited attempts remaining.

See Solution

Problem 541

(1 point)
Find the inverse Laplace transform $f(t)=\mathcal{L}^{-1}\{F(s)\}$ of the function $F(s)=\frac{1}{s}+\frac{5040}{s^{7}}$ . $f(t)=\mathcal{L}^{-1}\left\{\frac{1}{s}+\frac{5040}{s^{7}}\right\}=$ $\square$ help (formulas)
Preview My Answers Submit Answers
You have attempted this problem 0 times. You have unlimited attempts remaining.
Email Instructor

See Solution

Problem 542

Previous Problem Problem List Next Problem
Standard 17: Problem 3 (1 point)
Find the inverse Laplace transform $f(t)=\mathcal{L}^{-1}\{F(s)\}$ of the function $F(s)=-\left(\frac{1}{s^{2}+36}+\frac{8 s}{s^{2}+81}\right)$ . $f(t)=\mathcal{L}^{-1}\left\{-\left(\frac{1}{s^{2}+36}+\frac{8 s}{s^{2}+81}\right)\right\}=\square$ help (formulas)
Preview My Answers Submit Answers You have attempted this problem 0 times. You have unlimited attempts remainina.

See Solution

Problem 543

(1 point)
Consider the function $F(s)=\frac{4 s-10}{s^{2}-5 s+4}$ . a. Find the partial fraction decomposition of $F(s)$ : $\frac{4 s-10}{s^{2}-5 s+4}=\square+\square$ b. Find the inverse Laplace transform of $F(s)$ . $f(t)=\mathcal{L}^{-1}\{F(s)\}=$ $\square$ help (formulas)

See Solution

Problem 544

Differentiate implicitly to find $\frac{d y}{d x}$ . Then find the slope of the curve at the given point. $\begin{array}{l} y^{2}-x^{3}=22 ; \quad(3,-7) \\ \frac{d y}{d x}=\square \end{array}$
The slope of the graph at the given point is $\square$ (Type an integer or a simplified fraction.)

See Solution

Problem 545

Standard 17: Problem 6 (1 point)
Find the inverse Laplace transform $f(t)=\mathcal{L}^{-1}\{F(s)\}$ of the function $F(s)=\frac{6 s-23}{s^{2}-8 s+20}$ . $f(t)=\mathcal{L}^{-1}\left\{\frac{6 s-23}{s^{2}-8 s+20}\right\}=$ $\square$ help (formulas) Preview My Answers Submit Answers
You have attempted this problem 0 times. You have unlimited attempts remaining.

See Solution

Problem 546

An open-top box is to be made from a 12 -inch by 42 -inch piece of plastic by removing a square from each corner of the plastic and folding up the flaps on each side. What should be the length of the side $x$ of the square cut out of each corner to get a box with the maximum volume? You may enter an exact answer or round to the nearest hundredth.

See Solution

Problem 547

3. Antiderivatives and initial value problems (a) Let $f^{\prime \prime}(x)=-5$ i. Find $\int f^{\prime \prime}(x) d x$ . ii. Find $f^{\prime}(x)$ and $f(x)$ given that $f^{\prime}(1)=2$ and $f(1)=8$ . (b) Suppose you are driving at 12 meters $/ \mathrm{sec}$ . You see a turtle ahead, so you slam on the breaks, bringing your car to a complete stop in just 6 meters. Let's figure out what constant deceleration was needed to make this happen: i. Assume the constant acceleration is $a(t)=-k$ (negative becuase the car is slowing down). At the start of the problem you were driving at $12 \mathrm{~m} / \mathrm{s}$ , so the initial condition is $v(0)=12$ . Use this information to find the velocity function $v(t)$ . (Your answer will involve $k$ .) ii. Find the position function $s(t)$ given the initial condition $s(0)=0$ . (Your answer will still involve $k$ .) iii. Use the function $v(t)$ that you found above to determine the time $t$ at which the cal came to a stop. iv. Use the function $s(t)$ that you found above to find $k$ . (Hint: $s=6$ at the time wher the car came to a stop.) What constant deceleration did you use to make the car stop

See Solution

Problem 548

Part 1 of 3 HW Score: $61.11 \%, 11$ of 18 points Points: 0 of 1
The growth rate of a fungus vari $L(t)=2.4 t+0.75 \cos \left(\frac{2 \pi t}{24}\right)$ (a) Calculate the growth rate $\frac{\mathrm{dL}}{\mathrm{dt}}$ . (b) What is the largest growth rate of the microbe? What is the smallest growth rate? (a) Calculate the growth rate. $\frac{\mathrm{dL}}{\mathrm{dt}}=\square$
Type an exact answer using $\pi$ as needed.)

See Solution

Problem 549

Compute the following derivatives using the formulas below. $\begin{array}{l} m=\left.\frac{d}{d x}\left(5^{x}\right)\right|_{x=0} \approx 1.609 \\ \frac{d}{y^{x}}=m 5^{x} \end{array}$ (b) $\left.\frac{d}{d x}\left(5^{x}\right)\right|_{x=-4} \approx$ $\square$ (Round to two decimal places as needed.)

See Solution

Problem 550

Differentiate the following function. $\begin{array}{c} f(x)=e^{5 x^{2}+9 x} \\ \frac{d}{d x}\left(e^{5 x^{2}+9 x}\right)= \end{array}$ $\square$

See Solution

Problem 551

Given the definite integral $\int_{1}^{2}\left(1-\frac{8}{x^{3}}\right) d x$ : (a) The value of the definite integral is $\square$ . (b) The area of the region bounded by the $x$ -axis, the graph of the function, and the lines $x=1$ and $x=2$ is $\square$

See Solution

Problem 552

A driver accelerates when the car is traveling at a speed of 30 miles per hour (1.e., 44 feet per second). The velocity (in feet per second) function is $v(t)=44+2.2 t$ . (a) The car reaches the speed of 60 miles per hour (1.e., 88 feet per second) in $\square$ seconds. (a) Using a definite integral, it is determined that from the time the driver hits the gas pedal to the time the car reaches the speed of 60 miles per hour, the car has traveled $\square$ feet.

See Solution

Problem 553

Given $y=\sec (x)$ , find $\frac{d y}{d x}$ .
Answer Attempt 1 out of 2 $\frac{d y}{d x}=$ $\square$ Submit Answer

See Solution

Problem 554

Use the Fundamental Theorem of Calculus to find $f^{\prime}(x)$ , where $\begin{array}{r} f(x)=\int_{-4}^{x} \sqrt{t^{3}+64} d t \\ f^{\prime}(x)=\square \end{array}$

See Solution

Problem 555

$1,2,3,4,5$ , and 6 Specify whether each system is autonomous or nonautonomous, and whether it is linear or nonlinear. If it is linear, specify whether it is homogeneous or nonhomogeneous.
1. $d x / d t=x-y, \quad d y / d t=-3 t y+x$
HIDE ANSWER Answer: Linear, homogeneous, nonautonomous
2. $d y / d x=2 y, d z / d x=x-z+3$
3. $d y / d t=3 y z-2 z, \quad d z / d t=2 z+5 y$

See Solution

Problem 556

Evaluate. $\begin{array}{l} \int\left(6 x^{2} \cdot-4 x+4\right) d x \\ \int\left(6 x^{2}-4 x+4\right) d x=\square \end{array}$ $\square$ (Type an exact answer.)

See Solution

Problem 557

Evaluate. $\begin{array}{c} \int e^{8 x} d x \\ \int e^{8 x} d x= \end{array}$ $\square$

See Solution

Problem 558

Verify that the function satisfies the three hypotheses of Rolle's theorem on the given interval. Then find all numbers $c$ that satisfy the conclusion of Rolle's theorem. (Enter your answers as a commaseparated list.) $f(x)=3 x^{2}-6 x+4, \quad[-1,3]$ $c=$ $\square$

See Solution

Problem 559

12. (\ $pts) Find the length of the curve represented by the vector equation$ \vec{r}(t)=\left\langle t^{2},-9 t, 4 t^{\frac{2}{2}}\right\rangle $,$ 0 \leq t \leq 1$

See Solution

Problem 560

At 2:00 p.m. a car's speedometer reads $30 \mathrm{mi} / \mathrm{h}$ . At $2: 15 \mathrm{p} . \mathrm{m}$ . it reads $50 \mathrm{mi} / \mathrm{h}$ . Show that at some time between 2:00 and $2: 15$ the acceleration is exactly $80 \mathrm{mi} / \mathrm{h}^{2}$ . Let $v(t)$ be the velocity of the car $t$ hours after 2:00 p.m. Then $\frac{v(1 / 4)-v(0)}{1 / 4-0}=$ $\square$ . By the Mean Value Theorem, there is a number $c$ such that $0<c<$ $\square$ with $v^{\prime}(c)=$ $\square$ . Since $v^{\prime}(t)$ is the acceleration at time $t$ , the acceleration $c$ hours after 2:00 p.m. is exactly $80 \mathrm{mi} / \mathrm{h}^{2}$ . Need Help? Read It

See Solution

Problem 561

Question 7 (1 point) $\lim _{n \rightarrow \infty} \frac{3 n^{3}-5 n}{n^{3}-2 n^{2}+1}$ A. -5 B. -2 C. 1 D. 3

See Solution

Problem 562

Question 1 (1 point) $\checkmark$ Saved
Below is a graph of the derivative $y=f^{\prime}(x)$ . Use the graph to identify the location of the local minimum(s) of the function $f(x)$ . A. $x= \pm 2 \& 0$ B. $x= \pm 2$ c. $x=-3 \& 1$ D. $x=1$

See Solution

Problem 563

A rider's height, $h$ , in metres on a Ferris wheel is modelled by $h(t)=-49 \cos \left(\frac{2 \pi t}{142}\right)+52$ where $t$ is time in seconds. Solve for the AROC between $t=138$ and $t=140$ . Does this represent when the rider is going to the top of the ride, or coming back towards the ground? How do you know? Since the slope is negative, the rider is getting closer to the ground Since the slope is negative, the rider is heading backwards through time Since the slope is negative, the rider is moving to the top of the ride Since the slope is less than 1 , the rider is heading back towards the ground Previous Page Next Page Page 11 of 12

See Solution

Problem 564

b) (10 marks) Consider the following IVP problem: $\frac{1}{4} y^{\prime \prime}-y^{\prime}+10 y=(2 x-3)^{2} ; y(0)=1 ; y^{\prime}(0)=0$ i. Write the complementary equation for the given equation. ii. Write the auxiliary equation for the equation in part (i), solve it and hence obtain the general solution of the complementary equation. iii. Find a particular solution for the given equation. iv. Write the general solution for the given equation. v. Hence find the solution for the given IVP problem.

See Solution

Problem 565

Find the inflection points of $f(x)=x^{4}+x^{3}-18 x^{2}+4$ .
Enter the exact answers in increasing order. $\begin{array}{l} x=\square \\ x=\square \end{array}$

See Solution

Problem 566

Use the first derivative to find all critical points and use the second derivative to find all inflection points. Use a graph to identify each critical point as a local maximum, a local minimum, or neither. $f(x)=x^{4}-18 x^{2}+4$
NOTE: Enter the exact answers, or round them to three decimal places. Enter the number of critical points Choose one
Enter the number of inflection points Choose one

See Solution

Problem 567

1. Differentiate: $y=5^{\left(x^{2}-1\right)}$ A. $x^{2}(\ln 5)\left(5^{x^{2}-1}\right)$ B. $(\ln 5) 5^{\left(x^{2}-1\right)}$ C. $(2 x) 5^{\left(x^{2}-1\right)}$ D. $2 x(\ln 5)\left(5^{x^{2}-1}\right)$
2. Find $\frac{d y}{d x}$ if $y=e^{\cos \sqrt{x}}$ A. $(-\sin \sqrt{x}) e^{\cos \sqrt{x}}$ B. $\frac{-e^{\sin \sqrt{x}}}{2 \sqrt{x}}$ C. $\frac{-\sin \sqrt{x}}{2 \sqrt{x}}\left(e^{\cos \sqrt{x}}\right)$ D. $\left(-\frac{1}{2} \sin \sqrt{x}\right) e^{\cos \sqrt{x}-1}$
3. Find $f^{\prime}(x)$ for $f(x)=\sqrt{7+e^{4 x}}$ A. $\frac{1}{2 \sqrt{2 e^{2 x}}}$ B. $\frac{2 e^{4 x}}{\sqrt{7+e^{4 x}}}$ C. $\frac{5+e^{2 x}}{\sqrt{5+e^{2 x}}}$ D. $\frac{x e^{2 x-1}}{\sqrt{5+e^{2 x}}}$

See Solution

Problem 568

Question 9 1 pts
Use the Alternating Series Estimation Theorem to find the minimum number of terms of the infinite series $\sum_{n=1}^{\infty} \frac{2(-1)^{n}}{n^{3}}$ we need to add to approximate the sum of the series with $\mid$ error $\mid \leq .016$ . 8 10 4 6

See Solution

Problem 569

Name Anahi
8. Find $\frac{d y}{d x}$ for $y=\arccos \left(\frac{x}{3}\right)$ A. $\frac{-3}{\sqrt{x^{2}-9}}$ B. $\frac{-1}{\sqrt{9-x^{2}}}$ C. $\frac{-x}{\sqrt{9-x^{2}}}$ D. $\frac{3}{\sqrt{9-x^{2}}}$
9. If $f(x)=e^{5 x}$ , then $\left(f^{-1}\right)^{\prime}(x)=$ A. $\frac{1}{5 x}$ B. $\frac{1}{e^{5 x}}$ C. $\frac{1}{5 e^{5 x}}$ D. $-\frac{2}{e^{5 x}}$
Use the table below to answer question 10. \begin{tabular}{|c|c|c|c|c|c|c|} \hline $x$ & $F(x)$ & $F^{\prime}(x)$ & $F^{\prime \prime}(x)$ & $G(x)$ & $G^{\prime}(x)$ & $G^{\prime \prime}(x)$ \\ \hline 2 & 6 & 4 & 7 & -5 & 3 & 10 \\ \hline 5 & 2 & -4 & -2 & -3 & 2 & -4 \\ \hline \end{tabular}
10. If $H(x)=G(F(x))$ , then $H^{\prime}(5)=$ A. 40 B. -6 C. -14 D. -12

See Solution

Problem 570

4. If $y=\tan ^{-1}\left(\sin _{x} x\right)$ , then $\frac{d_{y}}{d_{x}}=$ A. $\left(\sec ^{-1}(\sin x)\right)^{2}$ C. $\left(\sec ^{-1}(\sin x)\right)^{2} \cos x$ B. D. $\frac{\mathrm{Cos}^{2}}{2+\sin ^{2} x}$
5. Let $f(x)=x^{4}+4 x-3$ , and let $g(x)$ denote the inverse of $f$ . Then $g^{\prime}(2)$ A. $\frac{1}{8}$ C. 8 B. $\frac{1}{32}$ D. 32 A. 2 B. $\frac{1}{2}$ D. $-\frac{1}{2}$ C. $\frac{10}{3}$ B. $-\frac{3}{10}$ D.

See Solution

Problem 571

Attempt 2: 2 attempts remaining.
Calculate the line integral $\int_{C} \frac{x y^{2}}{32} d s$ with respect to arc length over a curve $C$ that is the lower half of the circle $x^{2}+y^{2}=16$ .
The curve $C$ can be written with parametric equations $x(t)=4 \cos t \quad \text { and } y(t)=4 \sin t \quad \text { for } \pi \leq t \leq 2 \pi$
The resulting parameterized form of the line integral is $\int_{t_{1}}^{t_{2}} f(t) d t$ where $t_{1}=\pi$

See Solution

Problem 572

1 Points] DETAILS MY NOTES SCALCET9 4.XP.9.005.MI. ASK YOUR T
Find the most general antiderivative of the function. (Check your answer by differentiation. Use $C$ for the constant of the antiderivative.) $f(x)=(x+7)(2 x-11)$

See Solution

Problem 573

Substitution in the Indefinite Integral $\qquad$ Part 1. $\qquad$
Using the substitution: $u=x-4$ . Re-write the indefinite integral then evaluate in terms of $u$ . $\int \frac{x^{2}}{\sqrt{x-4}} d x=\int \square=\square$ $\square$ Note: answer should be in terms of $u$ only $\qquad$ Part 2. $\qquad$
Back substituting in the antiderivative you found in Part 1. above we have $\int \frac{x^{2}}{\sqrt{x-4}} d x=$ $\square$ Note: answer should be in terms of $x$ only

See Solution

Problem 574

Given the function $f(x)=3 \sin \left[(4 x+1)^{4}\right]$ , find $f^{\prime}(x)$ .
Answer Attempt 1 out of 3

See Solution

Problem 575

Question If $0=-2 x^{2}-x-5 y^{2}$ then find $\frac{d y}{d x}$ in terms of $x$ and $y$ .
Answer Attempt 1 out of 3

See Solution

Problem 576

Convert the integral $\int_{0}^{\sqrt{2}} \int_{-x}^{x} d y d x$ to polar coordinates and evaluate it (use $t$ for $\theta$ ): With $a=$ $\square$ $\square$ $\square$ and $d=$ $\square$ $\int_{0}^{\sqrt{2}} \int_{-x}^{x} d y d x=\int_{a}^{b} \int_{c}^{d} \square d r d t$ $\begin{aligned} = & \int_{a}^{b} \square d t \\ & =\square_{a}^{b} \\ & =\square . \end{aligned}$

See Solution

Problem 577

Find the mass of the rectangular region $0 \leq x \leq 3,0 \leq y \leq 3$ with density function $\rho(x, y)=3-y$ . $\square$

See Solution

Problem 578

Correct
Use integration by substitution to solve the integral below. Use C for the constant of integration. $\int \frac{-6(\ln (y))^{3}}{y} d y$
Answer

See Solution

Problem 579

Find $f^{\prime}(x)$ for $f^{\prime}(x)=\square \quad f(x)=\frac{5\left(x^{2}+2\right) \cot (x)}{1-\cos (x) \csc (x)}$

See Solution

Problem 580

b) $g(s)=16^{4} . \quad g^{\prime}(s)=$

See Solution

Problem 581

Chapter 5 - More Applicatlons 260 5.1 Exercises
In Exercises 1-12, determine the critical numbers of each function, then use the First Derivative Test to determine whether the function has a local maximum, a local minimum, or neither at each critical number. Confirm your answers graphically (1.) $f(x)=\frac{1}{3} x^{3}-x^{2}-3 x+3$
2. $f(x)=3 x^{4}-4 x^{3}-6 x^{2}+12 x$

See Solution

Problem 582

Evaluate the given integral by changing to polar coordinates. $\iint_{D} 2 x^{2} y d A$ , where $D$ is the top half of the disk with center the origin and radius 4.

See Solution

Problem 583

Evaluate the definite integral (if it exists) $\int_{e}^{e^{4}} \frac{-6}{x \sqrt{\ln (x)}} d x$
If the integral does not exist, type "DNE".

See Solution

Problem 584

Example 8: If $f(x)=e^{2 x}-3 x$ , find $f^{\prime}$ and $f^{\prime \prime}$

See Solution

Problem 585

1. a) Find the value of $m$ if $\lim _{x \rightarrow 0} \frac{m x+3 x^{2}}{4 x-8 x^{2}}=3$ .

See Solution

Problem 586

7.2a - Derivatives of the Sine an
1. Evaluate $\lim _{\theta \rightarrow 0} \frac{\sin 4 \theta}{\sin 6 \theta}=\frac{2}{3}$
2. Evaluate $\lim _{\theta \rightarrow 0} \frac{\sin \theta}{\theta+\tan \theta}$
3. Evaluate $\lim _{x \rightarrow 1} \frac{\sin (x-1)}{x^{2}+x-2}$

See Solution

Problem 587

Evaluate the definite integrals a) $\int_{\pi / 2}^{\pi} 5 \cos x d x=$ $\square$ b) $\int_{0}^{\pi / 4} 14 \sec ^{2} \theta d \theta=$ $\square$ c) $\int_{\pi / 6}^{\pi / 3} 7 \csc t \cot t d t=$ $\square$

See Solution

Problem 588

$=\lim _{x \rightarrow 0} \frac{e^{-2 x}+e^{x}}{2 e^{x}}$

See Solution

Problem 589

Logarithms as anti-derivatives. $\int \frac{-5}{x(\ln x)^{2}} d x=$ $\square$ Hint: Use the natural log function and substitution.

See Solution

Problem 590

(1 point) Evaluate the definite integral. $\int_{-6}^{-4}(x+4) e^{x^{2}+8 x+15} d x=$ $\square$

See Solution

Problem 591

If $f$ is continuous and $\int_{1}^{32} f(t) d t=10$ , find the integral $\int_{1}^{2} t^{4} f\left(t^{5}\right) d t$ . Answer: $\square$

See Solution

Problem 592

\begin{problem} The graph shown is used to find the following characteristics of the function:
1. The domain and range of the function.
2. The intercepts, if any.
3. Horizontal asymptotes, if any.
4. Vertical asymptotes, if any.
5. Oblique asymptotes, if any.
The domain of the function is $\square$ (Express your answer in interval notation. Use integers or fractions for any numbers in the expression.) \end{problem}

See Solution

Problem 593

3.6 Exercises
1. Find the derivatives of the following functions: (a) $f(s)=\frac{\sqrt{s}-1}{\sqrt{s}+1}$ (b) $f(x)=\left(\frac{1}{x}-x\right)\left(x^{2}+1\right)$ (c) $g(x)=\sec (2 x+1) \cot \left(x^{2}\right)$ (d) $s(t)=\frac{1+\csc t}{1-\csc t}$ (e) $f(x)=x^{3} \sin x \cos x$ . (f) $x^{1 / 2}+y^{1 / 2}=1$ .

See Solution

Problem 594

Evaluate the indefinite integral $\int \frac{-7 x}{1+x^{4}} d x$
Note: Any arbitrary constants used must be an upper-case "C".

See Solution

Problem 595

Evaluate the integral by any method. $\int \frac{\sin (3 x)}{7+\cos (3 x)} d x=$ $\square$ $+C$

See Solution

Problem 596

$K=\int_{0}^{\frac{\pi}{4}}(2 \cos 2 x-\cos 4 x) d x$

See Solution

Problem 597

2. $\left(x \sin \left(\frac{y}{x}\right)-y \cos \left(\frac{y}{x}\right)\right) d x+x \cos \left(\frac{y}{x}\right) d y=0$ diferansiyel denklemin genel çözümünü bulunuz (20p).

See Solution

Problem 598

(1 point)
Use the third-order Taylor polynonial for $e^{x} \sin (3 x)$ at $x=0$ to approximate $e^{\frac{1}{7}} \sin (3 / 7)$ by a rational number. $e^{\frac{1}{7}} \sin (3 / 7) \approx$ $\square$

See Solution

Problem 599

Find the differential of $y=\cos (-6 \pi x)$ .

See Solution

Problem 600

Compute (a) $\Delta y$ and (b) dy for the given values of $x$ and $\mathrm{dx}=\Delta x$ . $y=7-x^{2}, \quad x=-2, \quad \Delta x=.4$ (a) $\Delta y=$ $\square$ (b) $d y=$ 16 $\square$

See Solution

Calculus

Problem 501

Given the function f(x)=−3sin⁡(4+3x3)f(x)=-3 \sin \left(\sqrt{4+3 x^{3}}\right)f(x)=−3sin(4+3x3​), find f′(x)f^{\prime}(x)f′(x).Answer Attempt 1 out of 2 f′(x)=f^{\prime}(x)=f′(x)= Subnuit Answer

Problem 502

Problem 503

Problem 504

1. x3y+xy3=−8xyx^{3} y+x y^{3}=-8 x yx3y+xy3=−8xy

Problem 505

50 [chercher.]On donne I=[−2;12]\mathrm{I}=\left[-2 ; \frac{1}{2}\right]I=[−2;21​] et a=0a=0a=0. Sachant que T passe par A et par le point B(12;2)\mathrm{B}\left(\frac{1}{2} ; 2\right)B(21​;2), calculer f′(a)f^{\prime}(a)f′(a).

Problem 506

Problem 507

Problem 508

Question Watch Video ShowGiven the function f(x)=(−6+2x−3)(x2+8x−1+10)f(x)=\left(-6+2 x^{-3}\right)\left(x^{2}+8 x^{-1}+10\right)f(x)=(−6+2x−3)(x2+8x−1+10), fin in any form.Answer Attempt 1 out of 10 f′(x)=f^{\prime}(x)=f′(x)= □\square□ Submit

Problem 509

Problem 510

Problem 511

Given the function f(x)=cos⁡(πx)f(x)=\cos (\pi x)f(x)=cos(πx), compute the right-endpoint (Riemann) sum using n=3n=3n=3 on the interval [0,1][0,1][0,1]. R3=R_{3}=R3​= help (numbers)

Problem 512

Problem 513

Find the function f(x)f(x)f(x) described by the given initial value problem. f′′(x)=2sin⁡x,f′(π)=2,f(π)=4f(x)=□\begin{array}{l} f^{\prime \prime}(x)=2 \sin x, \quad f^{\prime}(\pi)=2, \quad f(\pi)=4 \\ f(x)=\square \end{array}f′′(x)=2sinx,f′(π)=2,f(π)=4f(x)=□​

Problem 514

Consider the function f(x)f(x)f(x) whose second derivative is f′′(x)=5x+8sin⁡(x)f^{\prime \prime}(x)=5 x+8 \sin (x)f′′(x)=5x+8sin(x). If f(0)=4f(0)=4f(0)=4 and f′(0)=4f^{\prime}(0)=4f′(0)=4, what is f(x)f(x)f(x) ? f(x)=f(x)=f(x)=

Problem 515

Find L−1{−3s−2+4(s−2)2+7s+5}L^{-1}\left\{\frac{-3}{s-2}+\frac{4}{(s-2)^{2}}+\frac{7}{s+5}\right\}L−1{s−2−3​+(s−2)24​+s+57​}

Problem 516

Find L−1{1s8+1s5+1s2}L^{-1}\left\{\frac{1}{s^{8}}+\frac{1}{s^{5}}+\frac{1}{s^{2}}\right\}L−1{s81​+s51​+s21​}

Problem 517

Find the general indefinite integral. Use an upper-case CCC for any arbitrary constants. ∫7z−3+4z−2+3z−1dz=\int 7 z^{-3}+4 z^{-2}+3 z^{-1} d z=∫7z−3+4z−2+3z−1dz= □\square□

Problem 518

Find the general indefinite integral. Use an upper-case CCC for any arbitrary constants. ∫(6−t)(−7+t2)dt=\int(6-t)\left(-7+t^{2}\right) d t=∫(6−t)(−7+t2)dt= □\square□

Problem 519

Find L−1{1s2+2s+37}L^{-1}\left\{\frac{1}{s^{2}+2 s+37}\right\}L−1{s2+2s+371​}

Problem 520

Find the general indefinite integral. Use an upper-case CCC for any arbitrary constants. ∫(x5+5+5x2+1)dx=\int\left(x^{5}+5+\frac{5}{x^{2}+1}\right) d x=∫(x5+5+x2+15​)dx= □\square□

Problem 521

Find the most general antiderivative of the function g(u)=5u5−3u2−6g(u)=5 u^{5}-3 u^{2}-6g(u)=5u5−3u2−6. Use an upper-case CCC for any arbitrary constants. G(u)=G(u)=G(u)=

Problem 522

Find fff if f′(x)=−5+9xf^{\prime}(x)=-5+9 xf′(x)=−5+9x and f(0)=2f(0)=2f(0)=2. f(x)=f(x)=f(x)=

Problem 523

F(x)=F(x)=F(x)=

Problem 524

[0/7 Points] DETAILS MY NOTESFind the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) g(x)=16−x23g(x)=\sqrt[3]{16-x^{2}}g(x)=316−x2​

Problem 525

Find lim⁡x→3x2−x−6x−3\lim _{x \rightarrow 3} \frac{x^{2}-x-6}{x-3}limx→3​x−3x2−x−6​

Problem 526

Example 6: (self-study) Find the abs. max and abs. min⁡\minmin values of fff on the given interval f(x)=x3−3x2+1,[−12,4]f(x)=x^{3}-3 x^{2}+1, \quad\left[-\frac{1}{2}, 4\right]f(x)=x3−3x2+1,[−21​,4] Solution:

Problem 527

Find the most general antiderivative of the function f(t)=−4cos⁡(t)−10sin⁡(t)f(t)=-4 \cos (t)-10 \sin (t)f(t)=−4cos(t)−10sin(t). Use an upper-case CCC for any arbitrary constants. F(t)=F(t)=F(t)=

Problem 528

Find lim⁡x→0+(cot⁡x)x\lim _{x \rightarrow 0^{+}}(\cot x)^{x}limx→0+​(cotx)x

Problem 529

Find the family of antiderivatives of the function f(x)=8.5x7F(x)=\begin{array}{l} f(x)=\frac{8.5}{\sqrt{x^{7}}} \\ F(x)= \end{array}f(x)=x7​8.5​F(x)=​

Problem 530

Consider the function f(x)=7x4−8x6f(x)=\frac{7}{x^{4}}-\frac{8}{x^{6}}f(x)=x47​−x68​. Let F(x)F(x)F(x) be the antiderivative of f(x)f(x)f(x) with F(1)=0F(1)=0F(1)=0. Compute F(2)F(2)F(2). F(2)=F(2)=F(2)= □\square□ Submit answer Next item wers Attempt 2 of 2

Problem 531

Problem 532

Find fff. f(x)=□f(x)=\squaref(x)=□

Problem 533

Differentiate implicitly to find d2ydx2\frac{d^{2} y}{d x^{2}}dx2d2y​. 3x3−y3=5d2ydx2=□\begin{array}{l} 3 x^{3}-y^{3}=5 \\ \frac{d^{2} y}{d x^{2}}=\square \end{array}3x3−y3=5dx2d2y​=□​

Problem 534

Problem 535

Problem 536

Problem 537

Problem 538

Problem 539

Problem 540

Previous Problem Problem List Next ProblemStandard 16: Problem 6 (1 point)Find the Laplace transform of 5cos⁡(at)−2emt5 \cos (a t)-2 e^{m t}5cos(at)−2emt : □\square□Preview My Answers Submit Answers You have attempted this problem 0 times. You have unlimited attempts remaining.

Problem 541

Problem 542

Problem 543

Problem 544

Problem 545

Problem 546

Problem 547

Problem 548

Problem 549

Problem 550

Differentiate the following function. f(x)=e5x2+9xddx(e5x2+9x)=\begin{array}{c} f(x)=e^{5 x^{2}+9 x} \\ \frac{d}{d x}\left(e^{5 x^{2}+9 x}\right)= \end{array}f(x)=e5x2+9xdxd​(e5x2+9x)=​ □\square□

Problem 551

Problem 552

Given the function $f(x)=-3 \sin \left(\sqrt{4+3 x^{3}}\right)$ , find $f^{\prime}(x)$ .
Answer Attempt 1 out of 2 $f^{\prime}(x)=$ Subnuit Answer

1. $x^{3} y+x y^{3}=-8 x y$

50 [chercher.]
On donne $\mathrm{I}=\left[-2 ; \frac{1}{2}\right]$ et $a=0$ . Sachant que T passe par A et par le point $\mathrm{B}\left(\frac{1}{2} ; 2\right)$ , calculer $f^{\prime}(a)$ .

Question Watch Video Show
Given the function $f(x)=\left(-6+2 x^{-3}\right)\left(x^{2}+8 x^{-1}+10\right)$ , fin in any form.
Answer Attempt 1 out of 10 $f^{\prime}(x)=$ $\square$ Submit

Given the function $f(x)=\cos (\pi x)$ , compute the right-endpoint (Riemann) sum using $n=3$ on the interval $[0,1]$ . $R_{3}=$ help (numbers)

Find the function $f(x)$ described by the given initial value problem. $\begin{array}{l} f^{\prime \prime}(x)=2 \sin x, \quad f^{\prime}(\pi)=2, \quad f(\pi)=4 \\ f(x)=\square \end{array}$

Consider the function $f(x)$ whose second derivative is $f^{\prime \prime}(x)=5 x+8 \sin (x)$ . If $f(0)=4$ and $f^{\prime}(0)=4$ , what is $f(x)$ ? $f(x)=$

Find $L^{-1}\left\{\frac{-3}{s-2}+\frac{4}{(s-2)^{2}}+\frac{7}{s+5}\right\}$

Find $L^{-1}\left\{\frac{1}{s^{8}}+\frac{1}{s^{5}}+\frac{1}{s^{2}}\right\}$

Find the general indefinite integral. Use an upper-case $C$ for any arbitrary constants. $\int 7 z^{-3}+4 z^{-2}+3 z^{-1} d z=$ $\square$

Find the general indefinite integral. Use an upper-case $C$ for any arbitrary constants. $\int(6-t)\left(-7+t^{2}\right) d t=$ $\square$

Find $L^{-1}\left\{\frac{1}{s^{2}+2 s+37}\right\}$

Find the general indefinite integral. Use an upper-case $C$ for any arbitrary constants. $\int\left(x^{5}+5+\frac{5}{x^{2}+1}\right) d x=$ $\square$

Find the most general antiderivative of the function $g(u)=5 u^{5}-3 u^{2}-6$ . Use an upper-case $C$ for any arbitrary constants. $G(u)=$

Find $f$ if $f^{\prime}(x)=-5+9 x$ and $f(0)=2$ . $f(x)=$

$F(x)=$

[0/7 Points] DETAILS MY NOTES
Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) $g(x)=\sqrt[3]{16-x^{2}}$

Find $\lim _{x \rightarrow 3} \frac{x^{2}-x-6}{x-3}$

Example 6: (self-study) Find the abs. max and abs. $\min$ values of $f$ on the given interval $f(x)=x^{3}-3 x^{2}+1, \quad\left[-\frac{1}{2}, 4\right]$ Solution:

Find the most general antiderivative of the function $f(t)=-4 \cos (t)-10 \sin (t)$ . Use an upper-case $C$ for any arbitrary constants. $F(t)=$

Find $\lim _{x \rightarrow 0^{+}}(\cot x)^{x}$

Find the family of antiderivatives of the function $\begin{array}{l} f(x)=\frac{8.5}{\sqrt{x^{7}}} \\ F(x)= \end{array}$

Consider the function $f(x)=\frac{7}{x^{4}}-\frac{8}{x^{6}}$ . Let $F(x)$ be the antiderivative of $f(x)$ with $F(1)=0$ . Compute $F(2)$ . $F(2)=$ $\square$ Submit answer Next item wers Attempt 2 of 2

Find $f$ . $f(x)=\square$

Differentiate implicitly to find $\frac{d^{2} y}{d x^{2}}$ . $\begin{array}{l} 3 x^{3}-y^{3}=5 \\ \frac{d^{2} y}{d x^{2}}=\square \end{array}$

Previous Problem Problem List Next Problem
Standard 16: Problem 6 (1 point)
Find the Laplace transform of $5 \cos (a t)-2 e^{m t}$ : $\square$
Preview My Answers Submit Answers You have attempted this problem 0 times. You have unlimited attempts remaining.

Differentiate the following function. $\begin{array}{c} f(x)=e^{5 x^{2}+9 x} \\ \frac{d}{d x}\left(e^{5 x^{2}+9 x}\right)= \end{array}$ $\square$

Given $y=\sec (x)$ , find $\frac{d y}{d x}$ .
Answer Attempt 1 out of 2 $\frac{d y}{d x}=$ $\square$ Submit Answer

Use the Fundamental Theorem of Calculus to find $f^{\prime}(x)$ , where $\begin{array}{r} f(x)=\int_{-4}^{x} \sqrt{t^{3}+64} d t \\ f^{\prime}(x)=\square \end{array}$

Evaluate. $\begin{array}{l} \int\left(6 x^{2} \cdot-4 x+4\right) d x \\ \int\left(6 x^{2}-4 x+4\right) d x=\square \end{array}$ $\square$ (Type an exact answer.)

Evaluate. $\begin{array}{c} \int e^{8 x} d x \\ \int e^{8 x} d x= \end{array}$ $\square$

12. (\ $pts) Find the length of the curve represented by the vector equation$ \vec{r}(t)=\left\langle t^{2},-9 t, 4 t^{\frac{2}{2}}\right\rangle $,$ 0 \leq t \leq 1$

Question 7 (1 point) $\lim _{n \rightarrow \infty} \frac{3 n^{3}-5 n}{n^{3}-2 n^{2}+1}$ A. -5 B. -2 C. 1 D. 3

Find the inflection points of $f(x)=x^{4}+x^{3}-18 x^{2}+4$ .
Enter the exact answers in increasing order. $\begin{array}{l} x=\square \\ x=\square \end{array}$

1 Points] DETAILS MY NOTES SCALCET9 4.XP.9.005.MI. ASK YOUR T
Find the most general antiderivative of the function. (Check your answer by differentiation. Use $C$ for the constant of the antiderivative.) $f(x)=(x+7)(2 x-11)$

Given the function $f(x)=3 \sin \left[(4 x+1)^{4}\right]$ , find $f^{\prime}(x)$ .
Answer Attempt 1 out of 3