Function

Problem 5801

A ball thrown from 5 feet high follows $f(x)=-0.6 x^{2}+2.7 x+5$ . Find its max height and distance from release.

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Problem 5802

Find the maximum height of the ball given the function $f(x)=-0.7 x^{2}+2.7 x+5$ and its distance from the throw point.

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Problem 5803

A ball is thrown from 6 feet high. Its height is modeled by $f(x)=-0.2 x^{2}+2.1 x+6$ . Find the max height and distance.

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Problem 5804

A ball is thrown from 5 ft high. Its height is modeled by $f(x)=-0.1 x^{2}+0.8 x+5$ . Find the max height and distance.

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Problem 5805

A ball is thrown from 8 feet high. Its height is modeled by $f(x)=-0.2 x^{2}+1.7 x+8$ . Find the maximum height and distance.

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Problem 5806

A ball is thrown from 7 feet high. Its height is modeled by $f(x)=-0.1 x^{2}+0.7 x+7$ . Find the max height and distance.

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Problem 5807

A ball is thrown from 8 feet high. Its height is modeled by $f(x)=-0.3 x^{2}+1.7 x+8$ . Find its max height and distance from release.

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Problem 5808

Calculate BMI with weight $24 \mathrm{~kg}$ and height $123 \mathrm{~cm}$ .

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Problem 5809

Find the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=7x+7$ , where $h \neq 0$ . Simplify your answer.

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Problem 5810

Calculate the difference quotient for $f(x)=x^{2}+5$ : find $\frac{f(x+h)-f(x)}{h}$ and simplify, where $h \neq 0$ .

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Problem 5811

Find the difference quotient $\frac{f(x+h)-f(x)}{h}$ for the function $f(x)=x^{2}-7x+2$ , where $h \neq 0$ .

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Problem 5812

Find the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=\frac{3x}{x+3}$ , with $h \neq 0$ . Simplify your answer.

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Problem 5813

Find the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=\frac{10}{x^{2}}$ , where $h \neq 0$ . Simplify your answer.

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Problem 5814

Find the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=\frac{11}{x^{2}}$ , simplifying your answer.

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Problem 5815

Find the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=\frac{5 x}{x+6}$ , where $h \neq 0$ . Simplify your answer.

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Problem 5816

Find the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=\frac{3x}{x+3}$ , $h \neq 0$ . Simplify your answer.

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Problem 5817

Find the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=\frac{9}{x^{2}}$ , simplifying where $h \neq 0$ .

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Problem 5818

Find the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=x^{2}-5 x+9$ , where $h \neq 0$ . Simplify your answer.

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Problem 5819

A farmer has 150 feet of fence for 1125 sq ft of adjoining squares. Find sides $x$ and $y$ . $x= y=$

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Problem 5820

Determine if the quadratic function $f(x)=3 x^{2}+12 x-7$ has a max or min value, then find that value.

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Problem 5821

Find the vertex coordinates of the parabola defined by $f(x)=-4(x+2)^{2}+3$ . Provide as an ordered pair.

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Problem 5822

Determine if the quadratic function $f(x)=3x^{2}+18x-9$ has a maximum or minimum value and find that value.

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Problem 5823

Identify if the function $f(x)=-3 x^{2}+6 x$ has a max or min value, then find that value.

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Problem 5824

A rifle fires bullets with speed $v=(-5.35 \times 10^{7}) t^{2}+(2.30 \times 10^{5}) t$ . Find acceleration, position, time, speed, and barrel length.

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Problem 5825

Sketch the graph of the quadratic function $f(x)=(x+2)^{2}-9$ . Find the axis of symmetry, domain, and range.

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Problem 5826

Sketch the graph of the quadratic function $f(x)=(x+1)^{2}-9$ . Find the axis of symmetry, domain, and range.

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Problem 5827

Sketch the graph of the quadratic $f(x)=(x-2)^{2}-9$ using its vertex and intercepts. Find the axis of symmetry, domain, and range.

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Problem 5828

Sketch the graph of $f(x)=(x-4)^{2}-9$ . Find the axis of symmetry, domain, and range.

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Problem 5829

Graph the function $f(x)=(x-1)^{2}+7$ using its vertex and $y$ -intercept to find the range.

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Problem 5830

Sketch the graph of $f(x)=(x-2)^{2}+4$ using its vertex and intercepts. Find the axis of symmetry, domain, and range.

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Problem 5831

Sketch the graph of $f(x)=3(x+1)^{2}-1$ , find the axis of symmetry, domain, and range. Use vertex and intercepts.

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Problem 5832

For the function $f(x)=x^{2}-4 x$ , find the x-intercepts, y-intercept, and graph it.

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Problem 5833

Which table shows values of $g$ with $\lim_{x \to 7} g(x) = 6$ ? Options: (A), (B), (C), (D).

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Problem 5834

What does $\lim _{x \rightarrow 3} f(x)=5$ mean? Choose the correct interpretation: (A), (B), (C), or (D).

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Problem 5835

A car's distance is $s(t)$ in feet after $t$ seconds. Estimate its velocity at $t=6$ using options (A) to (D).

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Problem 5836

Find $\lim _{x \rightarrow 2^{+}} f(x)$ for the piecewise function: $f(x)=\{5x-3 \text{ if } x<2, 9 \text{ if } x=2, 4x+3 \text{ if } x>2\}$ .

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Problem 5837

Given the table of values for $f(x)$ at $x$ near 4, what limit conclusion is supported? (A) $\lim _{x \rightarrow 4} f(x)=6$ , (B) $\lim _{x \rightarrow 4} f(x)=7$ , (C) $\lim _{x \rightarrow 4^{-}} f(x)=6$ and $\lim _{x \rightarrow 4^{+}} f(x)=7$ , (D) $\lim _{x \rightarrow 4^{-}} f(x)=7$ and $\lim _{x \rightarrow 4^{+}} f(x)=6$ .

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Problem 5838

Given the table of $x$ and $f(x)$ values, which limit conclusion about $f(x)$ as $x$ approaches 6 is correct? (A) $\lim _{x \rightarrow 6} f(x)=0$ (B) $\lim _{x \rightarrow 6} f(x)=6$ (C) $\lim _{x \rightarrow 6} f(x)=10$ (D) $\lim _{x \rightarrow 6} f(x)$ does not exist.

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Problem 5839

Given the table values of $f(x)$ for $x$ near 4, which limit conclusion is correct? (A) $\lim _{x \rightarrow 4} f(x)=6$ (B) $\lim _{x \rightarrow 4} f(x)=7$ (C) $\lim _{x \rightarrow 4^{-}} f(x)=6$ and $\lim _{x \rightarrow 4^{+}} f(x)=7$ (D) $\lim _{x \rightarrow 4^{-}} f(x)=7$ and $\lim _{x \rightarrow 4^{+}} f(x)=6$

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Problem 5840

Find $\lim _{x \rightarrow 2}(h(x)(5 f(x)+g(x)))$ given $f(2)=3$ , $g(2)=-6$ , $h(2)=-3$ , limits at $x=2$ .

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Problem 5841

Find $\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}-2 x-15}$ . Options: (A) 0 (B) $\frac{3}{5}$ (C) $\frac{3}{4}$ (D) 1 (E) nonexistent.

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Problem 5842

Find $\lim _{x \rightarrow 0} \frac{\tan (2 x)}{6 x \sec (3 x)}$ . Choose from (A) 0, (B) $\frac{1}{6}$ , (C) $\frac{1}{3}$ , (D) nonexistent.

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Problem 5843

Find $\lim _{x \rightarrow 2} f(x)$ for the function $f(x)=\frac{x^{2}-4}{x^{2}+x-6}$ . Choices: (A) 0, (B) $\frac{2}{3}$ , (C) $\frac{4}{5}$ , (D) nonexistent.

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Problem 5844

Find the value of $k$ such that $\lim _{x \rightarrow 2} f(x)=3$ for $f(x)=\frac{(x-2)(x^{2}-k^{2})}{(x^{2}-4)(x-k)}$ .

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Problem 5845

Find $\lim _{x \rightarrow \frac{\pi}{4}} g(x)$ for $g(x)=\frac{\cos x-\sin x}{1-2 \sin ^{2} x}$ . Options: (A) 0 (B) $\frac{1}{\sqrt{2}}$ (C) $\sqrt{2}$ (D) Limit does not exist.

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Problem 5846

Find $\lim _{x \rightarrow 1} f(x)$ for $f(x)=\frac{x^{2}-1}{\sqrt{x}-1}$ . Choices: (A) 4, (B) 2, (C) 0, (D) nonexistent.

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Problem 5847

Identify the graph of $f(x)=\frac{1}{3} x$ and its parent function. Describe the transformation.

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Problem 5848

Which function has a horizontal asymptote at 4? A. $f(x)=2(3)^{x}+4$ B. $f(x)=2 x-4$ C. $f(x)=3(2)^{x}-4$ D. $f(x)=-3 x+4$

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Problem 5849

Which function has a horizontal asymptote at 4? A. $f(x)=2(3)^{x}+4$ B. $f(x)=2 x-4$ C. $f(x)=3(2)^{x}-4$ D. $f(x)=-3 x+4$

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Problem 5850

Complete the table for the function $y=-\frac{2}{3} x+7$ with domain $\{-12,-6,3,15\}$ .

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Problem 5851

Find the weight range $w$ for a healthy BMI (19-25) at heights: (a) 75 in., (b) 74 in., (c) 78 in. Round to nearest lb.

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Problem 5852

Laurie's candy dispenser dispenses candy tripling for each pound per square inch of pressure. Is this a relation, function, both, or neither?

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Problem 5853

Solve the equation $C=\pi d$ for $d$ . What is $d$ in terms of $C$ ?

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Problem 5854

Find the weight range $w$ for a healthy BMI (19-25) using $\mathrm{BMI}=\frac{704 \times \text{weight}}{\text{height}^2}$ for heights: 75 in, 74 in, 78 in.

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Problem 5855

Find the production level $x$ where revenue $R=26x$ is less than cost $C=91,000+19x$ . What is $x$ ?

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Problem 5856

Find the production level $x$ where revenue $R=29x$ is less than cost $C=90,000+19x$ . When does R < C?

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Problem 5857

Find the weight range $w$ (to nearest pound) for a healthful BMI (19-25) using $BMI=\frac{704 \times(\text{weight})}{(\text{height})^2}$ . Heights: (a) 66 in, (b) 78 in, (c) 73 in.

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Problem 5858

An alloy is made by mixing 28g of 15% copper and 100g of 55% copper. Find the grams and percentage of copper in the mixture.

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Problem 5859

Nicole and Chris each deposit \$90,000 at 3\% interest. Calculate their interest for the first three years and compare.

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Problem 5860

Bestimmen Sie die Funktionsgleichungen für die angegebenen Punkte und Extrempunkte bei ganzrationalen Funktionen.

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Problem 5861

Determine the other trigonometric functions for $\theta$ given that $\tan \theta=-\frac{1}{6}$ and $\sin \theta>0$ .

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Problem 5862

Nicole and Chris each deposit \$20,000 at 2\% interest. Find their earnings for 3 years and compare.

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Problem 5863

Find the exact value of $\tan \left(-\frac{\pi}{3}\right)$ using reference angles.

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Problem 5864

Find the exact value of $\sin \left(-300^{\circ}\right)$ using reference angles.

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Problem 5865

Debra deposits \$30,000 at 4\% compounded annually, while Dan uses simple interest. Calculate their interest for 3 years and compare.

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Problem 5866

Find the exact value of $\cos \left(-\frac{\pi}{3}\right)$ using reference angles.

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Problem 5867

Debra and Dan each deposit \$30,000 at 4\% interest. Calculate their yearly interest for 3 years and compare.

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Problem 5868

Amy deposits \$60,000 at 3\% annual compound interest, Bill at 3\% simple interest. Calculate their interest for 3 years.

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Problem 5869

Find the derivative of $y=\frac{1}{x}$ , calculate $\lim_{x \to \infty} \frac{-4x}{7x-3}$ , and find two numbers with a difference of 4 that minimize their product.

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Problem 5870

Create a table and graph for $g(x)=\frac{2}{x}$ , then describe the graph in detail.

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Problem 5871

Find the average rate of change of $f(x)=\sin x$ from $x_{1}=\frac{\pi}{4}$ to $x_{2}=\frac{3\pi}{2}$ .

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Problem 5872

Find the limit of $\frac{f(x+h)-f(x)}{h}$ for $f(x)=x^{2}+1$ as $h \neq 0$ .

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Problem 5873

Differentiate the following using the Product Rule:
1. $y=x^{2}(x+1)$
2. $y=(x^{2}+3)(x+6)$
3. $y=\sqrt{x}(x^{3}+6)$
4. $y=(2 x^{2}+4 x-3)(3 x+4)$

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Problem 5874

Bestimmen Sie die Hochpunkt-Koordinaten der Funktion $f(x)=x^{4}-\frac{4}{3} x^{3}-4 x^{2}$ .

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Problem 5875

Find $f[g(x)]$ and $g[f(x)]$ for $f(x)=\frac{4}{x+3}$ and $g(x)=x^{2}-3$ .

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Problem 5876

Differentiate these functions using the quotient rule: $y=\frac{x+2}{x+3}$ , $y=\frac{1}{x(2x+1)}$ , $y=\frac{4x+1}{3x+8}$ , $y=\frac{2-3x}{1+x}$ .

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Problem 5877

Ann deposits \$40,000 at 4\% compounded annually, while Jim deposits \$40,000 at 4\% simple interest. Calculate their interest for 3 years and compare.

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Problem 5878

Ann deposits \$40,000 at 4% annual compound interest. Jim deposits \$40,000 at 4% simple interest. Find their interest for 3 years.

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Problem 5879

Ann invests \$40,000 at 4% compounded annually. Jim invests \$40,000 at 4% simple interest. Calculate their interest for 3 years and compare.

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Problem 5880

Record the truck's mileage at various times. Identify independent (time) and dependent (mileage) variables.

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Problem 5881

Identify values to exclude from the domain of $\frac{x^{2}}{x^{2}+16}$ . Options: $x=5$ , $x=4$ , $x=0$ , $x=-4$ . Select all that apply.

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Problem 5882

Find the domain of $x$ for the expression $\frac{4}{x-19}$ .

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Problem 5883

Find the domain of $x$ in the expression $\frac{x}{x+79}$ .

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Problem 5884

Find the limit as $x$ approaches 3 for the expression $\frac{4x+2}{x+4}$ .

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Problem 5885

Calculate and compare interest for Laura's compound and Eric's simple interest on \$70,000 at 3\% for 3 years.

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Problem 5886

Ravi buys a laptop for R\$7000, deposits R\$1400, and pays 12\% annual interest compounded quarterly for 3 years. Find his monthly payment.

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Problem 5887

Determine the range of the function $f(x)=3x+2$ for the domain $\{0,2,4,6\}$ .

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Problem 5888

Determine the range of the function $g(x) = x^{2}$ for the domain $-2 \leq x \leq 2$ .

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Problem 5889

Find the composite functions for: a) $f(x)=3x+2$ , b) $g(h(x))$ , c) $h(g(f(x)))$ .

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Problem 5890

Pete has $x$ mice. After getting 4 more, he has $x + 4$ . Mal has $x + 4 - 15$ . If Mal has 10 mice, find $x$ .

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Problem 5891

Find the inverse function $f^{-1}(x)$ and its domain and range for $f(x)=\sqrt{x}+4$ .

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Problem 5892

Find $f^{-1}(x)$ , and state the domain and range of $f^{-1}(x)$ for $f(x)=\sqrt{12}(x+5)$ .

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Problem 5893

(1 point)
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. $\begin{array}{l} f(x)=\sum_{n=0}^{\infty} \square(x)=\frac{x^{6}}{5 x^{4}+1} \\ f(x)=\square+\square+\square+\square+\square+\cdots \end{array}$
The open interval of convergence is: $\square$ (Give your answer in interval notation.).

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Problem 5894

Owl uwo email Calculus Textbook Bio Mindtap 1001 Textbook He... Achieve Chemistry Module Health Sci 1001A... 11A Midterm Exam Oct2024.pdf 12 / 16 118\% October 2024 Biology 1001A Midterm Exam Page 12 of 16
30. Cell growth and cell replication are essential for the development of multicellular organisms. The surface area to volume ratio (SA/V) is related to cell growth and replication. Imagine a cell that has just completed cytokinesis at time 0 . It then continues to grow from timeline 0-200 mins after which it enters the mitotic phase of the cell cycle. At time 300 mins , it undergoes cytokinesis again.
Which of the following graphs depict the change in the SA/V ratio of the cell from time 0-300 mins?
C A. A B. B C. C D. D

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Problem 5895

Use l'Hôpital's rule to find the following limit. $\lim _{x \rightarrow 10^{+}}\left(\frac{1}{\ln (x-9)}-\frac{1}{x-10}\right)$ $\lim _{x \rightarrow 10^{+}}\left(\frac{1}{\ln (x-9)}-\frac{1}{x-10}\right)=$ $\square$ (Type an integer or a simplified fraction.)

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Problem 5896

Evaluate exactly, using the Fundamental Theorem of Calculus: $\int_{0}^{a}\left(\frac{x^{2}}{9}+6 x\right) d x=$ $\square$

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Problem 5897

The average cost per item to produce $q$ items is given by $a(q)=0.02 q^{2}-1.2 q+29, \quad \text { for } \quad q>0$
What is the total cost, $C(q)$ , of producing $q$ goods? $C(q)=$ $\square$ What is the minimum marginal cost? minimum MC = $\square$ (Be sure you can say what the practical interpretation of this result is!) At what production level is the average cost a minimum? $q=\square$
What is the lowest average cost? minimum average cost = $\square$ Compute the marginal cost at $q=30$ . $M C(30)=$ $\square$

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Problem 5898

Question 12 of 13, Step 1 of 1 8/13 Correct
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations $y=\frac{4}{(x+4)^{2}}, x=0, x=12$ , and $y=0$ about the $y$ -axis. Write the exact answer. Do not round.
Answer Keyp Keyboard Short $V=\square$

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Problem 5899

The number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate parameter of $6.1 \%$ per hour. How many hours does it take for the size of the sample to double? Note: This is a continuous exponential growth model. Do not round any intermediate computations, and round your answer to the nearest hundredth.

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Problem 5900

2) Given the polar equation $r=6 \cos \theta$ Calculate the slope of the tangentat $\theta=\pi / 3$

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1 ...56 57 58 59 60 61 62 ...103

Function

Problem 5801

A ball thrown from 5 feet high follows f(x)=−0.6x2+2.7x+5f(x)=-0.6 x^{2}+2.7 x+5f(x)=−0.6x2+2.7x+5. Find its max height and distance from release.

Problem 5802

Find the maximum height of the ball given the function f(x)=−0.7x2+2.7x+5f(x)=-0.7 x^{2}+2.7 x+5f(x)=−0.7x2+2.7x+5 and its distance from the throw point.

Problem 5803

A ball is thrown from 6 feet high. Its height is modeled by f(x)=−0.2x2+2.1x+6f(x)=-0.2 x^{2}+2.1 x+6f(x)=−0.2x2+2.1x+6. Find the max height and distance.

Problem 5804

A ball is thrown from 5 ft high. Its height is modeled by f(x)=−0.1x2+0.8x+5f(x)=-0.1 x^{2}+0.8 x+5f(x)=−0.1x2+0.8x+5. Find the max height and distance.

Problem 5805

A ball is thrown from 8 feet high. Its height is modeled by f(x)=−0.2x2+1.7x+8f(x)=-0.2 x^{2}+1.7 x+8f(x)=−0.2x2+1.7x+8. Find the maximum height and distance.

Problem 5806

A ball is thrown from 7 feet high. Its height is modeled by f(x)=−0.1x2+0.7x+7f(x)=-0.1 x^{2}+0.7 x+7f(x)=−0.1x2+0.7x+7. Find the max height and distance.

Problem 5807

A ball is thrown from 8 feet high. Its height is modeled by f(x)=−0.3x2+1.7x+8f(x)=-0.3 x^{2}+1.7 x+8f(x)=−0.3x2+1.7x+8. Find its max height and distance from release.

Problem 5808

Calculate BMI with weight 24 kg24 \mathrm{~kg}24 kg and height 123 cm123 \mathrm{~cm}123 cm.

Problem 5809

Find the difference quotient f(x+h)−f(x)h\frac{f(x+h)-f(x)}{h}hf(x+h)−f(x)​ for f(x)=7x+7f(x)=7x+7f(x)=7x+7, where h≠0h \neq 0h=0. Simplify your answer.

Problem 5810

Calculate the difference quotient for f(x)=x2+5f(x)=x^{2}+5f(x)=x2+5: find f(x+h)−f(x)h\frac{f(x+h)-f(x)}{h}hf(x+h)−f(x)​ and simplify, where h≠0h \neq 0h=0.

Problem 5811

Find the difference quotient f(x+h)−f(x)h\frac{f(x+h)-f(x)}{h}hf(x+h)−f(x)​ for the function f(x)=x2−7x+2f(x)=x^{2}-7x+2f(x)=x2−7x+2, where h≠0h \neq 0h=0.

Problem 5812

Find the difference quotient f(x+h)−f(x)h\frac{f(x+h)-f(x)}{h}hf(x+h)−f(x)​ for f(x)=3xx+3f(x)=\frac{3x}{x+3}f(x)=x+33x​, with h≠0h \neq 0h=0. Simplify your answer.

Problem 5813

Find the difference quotient f(x+h)−f(x)h\frac{f(x+h)-f(x)}{h}hf(x+h)−f(x)​ for f(x)=10x2f(x)=\frac{10}{x^{2}}f(x)=x210​, where h≠0h \neq 0h=0. Simplify your answer.

Problem 5814

Find the difference quotient f(x+h)−f(x)h\frac{f(x+h)-f(x)}{h}hf(x+h)−f(x)​ for f(x)=11x2f(x)=\frac{11}{x^{2}}f(x)=x211​, simplifying your answer.

Problem 5815

Find the difference quotient f(x+h)−f(x)h\frac{f(x+h)-f(x)}{h}hf(x+h)−f(x)​ for f(x)=5xx+6f(x)=\frac{5 x}{x+6}f(x)=x+65x​, where h≠0h \neq 0h=0. Simplify your answer.

Problem 5816

Find the difference quotient f(x+h)−f(x)h\frac{f(x+h)-f(x)}{h}hf(x+h)−f(x)​ for f(x)=3xx+3f(x)=\frac{3x}{x+3}f(x)=x+33x​, h≠0h \neq 0h=0. Simplify your answer.

Problem 5817

Find the difference quotient f(x+h)−f(x)h\frac{f(x+h)-f(x)}{h}hf(x+h)−f(x)​ for f(x)=9x2f(x)=\frac{9}{x^{2}}f(x)=x29​, simplifying where h≠0h \neq 0h=0.

Problem 5818

Find the difference quotient f(x+h)−f(x)h\frac{f(x+h)-f(x)}{h}hf(x+h)−f(x)​ for f(x)=x2−5x+9f(x)=x^{2}-5 x+9f(x)=x2−5x+9, where h≠0h \neq 0h=0. Simplify your answer.

Problem 5819

A farmer has 150 feet of fence for 1125 sq ft of adjoining squares. Find sides xxx and yyy. x=y= x= y= x=y=

Problem 5820

Determine if the quadratic function f(x)=3x2+12x−7f(x)=3 x^{2}+12 x-7f(x)=3x2+12x−7 has a max or min value, then find that value.

Problem 5821

Find the vertex coordinates of the parabola defined by f(x)=−4(x+2)2+3f(x)=-4(x+2)^{2}+3f(x)=−4(x+2)2+3. Provide as an ordered pair.

Problem 5822

Determine if the quadratic function f(x)=3x2+18x−9f(x)=3x^{2}+18x-9f(x)=3x2+18x−9 has a maximum or minimum value and find that value.

Problem 5823

Identify if the function f(x)=−3x2+6xf(x)=-3 x^{2}+6 xf(x)=−3x2+6x has a max or min value, then find that value.

Problem 5824

A rifle fires bullets with speed v=(−5.35×107)t2+(2.30×105)tv=(-5.35 \times 10^{7}) t^{2}+(2.30 \times 10^{5}) tv=(−5.35×107)t2+(2.30×105)t. Find acceleration, position, time, speed, and barrel length.

Problem 5825

Sketch the graph of the quadratic function f(x)=(x+2)2−9f(x)=(x+2)^{2}-9f(x)=(x+2)2−9. Find the axis of symmetry, domain, and range.

Problem 5826

Sketch the graph of the quadratic function f(x)=(x+1)2−9f(x)=(x+1)^{2}-9f(x)=(x+1)2−9. Find the axis of symmetry, domain, and range.

Problem 5827

Sketch the graph of the quadratic f(x)=(x−2)2−9f(x)=(x-2)^{2}-9f(x)=(x−2)2−9 using its vertex and intercepts. Find the axis of symmetry, domain, and range.

Problem 5828

Sketch the graph of f(x)=(x−4)2−9f(x)=(x-4)^{2}-9f(x)=(x−4)2−9. Find the axis of symmetry, domain, and range.

Problem 5829

Graph the function f(x)=(x−1)2+7f(x)=(x-1)^{2}+7f(x)=(x−1)2+7 using its vertex and yyy-intercept to find the range.

Problem 5830

Sketch the graph of f(x)=(x−2)2+4f(x)=(x-2)^{2}+4f(x)=(x−2)2+4 using its vertex and intercepts. Find the axis of symmetry, domain, and range.

Problem 5831

Sketch the graph of f(x)=3(x+1)2−1f(x)=3(x+1)^{2}-1f(x)=3(x+1)2−1, find the axis of symmetry, domain, and range. Use vertex and intercepts.

Problem 5832

For the function f(x)=x2−4xf(x)=x^{2}-4 xf(x)=x2−4x, find the x-intercepts, y-intercept, and graph it.

Problem 5833

Which table shows values of ggg with lim⁡x→7g(x)=6\lim_{x \to 7} g(x) = 6limx→7​g(x)=6? Options: (A), (B), (C), (D).

Problem 5834

What does lim⁡x→3f(x)=5\lim _{x \rightarrow 3} f(x)=5limx→3​f(x)=5 mean? Choose the correct interpretation: (A), (B), (C), or (D).

Problem 5835

A car's distance is s(t)s(t)s(t) in feet after ttt seconds. Estimate its velocity at t=6t=6t=6 using options (A) to (D).

Problem 5836

Find lim⁡x→2+f(x)\lim _{x \rightarrow 2^{+}} f(x)limx→2+​f(x) for the piecewise function: f(x)={5x−3 if x<2,9 if x=2,4x+3 if x>2}f(x)=\{5x-3 \text{ if } x<2, 9 \text{ if } x=2, 4x+3 \text{ if } x>2\}f(x)={5x−3 if x<2,9 if x=2,4x+3 if x>2}.

Problem 5837

Problem 5838

Problem 5839

Problem 5840

Find lim⁡x→2(h(x)(5f(x)+g(x)))\lim _{x \rightarrow 2}(h(x)(5 f(x)+g(x)))limx→2​(h(x)(5f(x)+g(x))) given f(2)=3f(2)=3f(2)=3, g(2)=−6g(2)=-6g(2)=−6, h(2)=−3h(2)=-3h(2)=−3, limits at x=2x=2x=2.

Problem 5841

Find lim⁡x→−3x2−9x2−2x−15\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}-2 x-15}limx→−3​x2−2x−15x2−9​. Options: (A) 0 (B) 35\frac{3}{5}53​ (C) 34\frac{3}{4}43​ (D) 1 (E) nonexistent.

A ball thrown from 5 feet high follows $f(x)=-0.6 x^{2}+2.7 x+5$ . Find its max height and distance from release.

Find the maximum height of the ball given the function $f(x)=-0.7 x^{2}+2.7 x+5$ and its distance from the throw point.

A ball is thrown from 6 feet high. Its height is modeled by $f(x)=-0.2 x^{2}+2.1 x+6$ . Find the max height and distance.

A ball is thrown from 5 ft high. Its height is modeled by $f(x)=-0.1 x^{2}+0.8 x+5$ . Find the max height and distance.

A ball is thrown from 8 feet high. Its height is modeled by $f(x)=-0.2 x^{2}+1.7 x+8$ . Find the maximum height and distance.

A ball is thrown from 7 feet high. Its height is modeled by $f(x)=-0.1 x^{2}+0.7 x+7$ . Find the max height and distance.

A ball is thrown from 8 feet high. Its height is modeled by $f(x)=-0.3 x^{2}+1.7 x+8$ . Find its max height and distance from release.

Calculate BMI with weight $24 \mathrm{~kg}$ and height $123 \mathrm{~cm}$ .

Find the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=7x+7$ , where $h \neq 0$ . Simplify your answer.

Calculate the difference quotient for $f(x)=x^{2}+5$ : find $\frac{f(x+h)-f(x)}{h}$ and simplify, where $h \neq 0$ .

Find the difference quotient $\frac{f(x+h)-f(x)}{h}$ for the function $f(x)=x^{2}-7x+2$ , where $h \neq 0$ .

Find the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=\frac{3x}{x+3}$ , with $h \neq 0$ . Simplify your answer.

Find the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=\frac{10}{x^{2}}$ , where $h \neq 0$ . Simplify your answer.

Find the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=\frac{11}{x^{2}}$ , simplifying your answer.

Find the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=\frac{5 x}{x+6}$ , where $h \neq 0$ . Simplify your answer.

Find the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=\frac{3x}{x+3}$ , $h \neq 0$ . Simplify your answer.

Find the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=\frac{9}{x^{2}}$ , simplifying where $h \neq 0$ .

Find the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=x^{2}-5 x+9$ , where $h \neq 0$ . Simplify your answer.

A farmer has 150 feet of fence for 1125 sq ft of adjoining squares. Find sides $x$ and $y$ . $x= y=$

Determine if the quadratic function $f(x)=3 x^{2}+12 x-7$ has a max or min value, then find that value.

Find the vertex coordinates of the parabola defined by $f(x)=-4(x+2)^{2}+3$ . Provide as an ordered pair.

Determine if the quadratic function $f(x)=3x^{2}+18x-9$ has a maximum or minimum value and find that value.

Identify if the function $f(x)=-3 x^{2}+6 x$ has a max or min value, then find that value.

A rifle fires bullets with speed $v=(-5.35 \times 10^{7}) t^{2}+(2.30 \times 10^{5}) t$ . Find acceleration, position, time, speed, and barrel length.

Sketch the graph of the quadratic function $f(x)=(x+2)^{2}-9$ . Find the axis of symmetry, domain, and range.

Sketch the graph of the quadratic function $f(x)=(x+1)^{2}-9$ . Find the axis of symmetry, domain, and range.

Sketch the graph of the quadratic $f(x)=(x-2)^{2}-9$ using its vertex and intercepts. Find the axis of symmetry, domain, and range.

Sketch the graph of $f(x)=(x-4)^{2}-9$ . Find the axis of symmetry, domain, and range.

Graph the function $f(x)=(x-1)^{2}+7$ using its vertex and $y$ -intercept to find the range.

Sketch the graph of $f(x)=(x-2)^{2}+4$ using its vertex and intercepts. Find the axis of symmetry, domain, and range.

Sketch the graph of $f(x)=3(x+1)^{2}-1$ , find the axis of symmetry, domain, and range. Use vertex and intercepts.

For the function $f(x)=x^{2}-4 x$ , find the x-intercepts, y-intercept, and graph it.

Which table shows values of $g$ with $\lim_{x \to 7} g(x) = 6$ ? Options: (A), (B), (C), (D).

What does $\lim _{x \rightarrow 3} f(x)=5$ mean? Choose the correct interpretation: (A), (B), (C), or (D).

A car's distance is $s(t)$ in feet after $t$ seconds. Estimate its velocity at $t=6$ using options (A) to (D).

Find $\lim _{x \rightarrow 2^{+}} f(x)$ for the piecewise function: $f(x)=\{5x-3 \text{ if } x<2, 9 \text{ if } x=2, 4x+3 \text{ if } x>2\}$ .

Find $\lim _{x \rightarrow 2}(h(x)(5 f(x)+g(x)))$ given $f(2)=3$ , $g(2)=-6$ , $h(2)=-3$ , limits at $x=2$ .

Find $\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}-2 x-15}$ . Options: (A) 0 (B) $\frac{3}{5}$ (C) $\frac{3}{4}$ (D) 1 (E) nonexistent.

Find $\lim _{x \rightarrow 0} \frac{\tan (2 x)}{6 x \sec (3 x)}$ . Choose from (A) 0, (B) $\frac{1}{6}$ , (C) $\frac{1}{3}$ , (D) nonexistent.

Find $\lim _{x \rightarrow 2} f(x)$ for the function $f(x)=\frac{x^{2}-4}{x^{2}+x-6}$ . Choices: (A) 0, (B) $\frac{2}{3}$ , (C) $\frac{4}{5}$ , (D) nonexistent.

Find the value of $k$ such that $\lim _{x \rightarrow 2} f(x)=3$ for $f(x)=\frac{(x-2)(x^{2}-k^{2})}{(x^{2}-4)(x-k)}$ .

Find $\lim _{x \rightarrow \frac{\pi}{4}} g(x)$ for $g(x)=\frac{\cos x-\sin x}{1-2 \sin ^{2} x}$ . Options: (A) 0 (B) $\frac{1}{\sqrt{2}}$ (C) $\sqrt{2}$ (D) Limit does not exist.

Find $\lim _{x \rightarrow 1} f(x)$ for $f(x)=\frac{x^{2}-1}{\sqrt{x}-1}$ . Choices: (A) 4, (B) 2, (C) 0, (D) nonexistent.

Identify the graph of $f(x)=\frac{1}{3} x$ and its parent function. Describe the transformation.

Which function has a horizontal asymptote at 4? A. $f(x)=2(3)^{x}+4$ B. $f(x)=2 x-4$ C. $f(x)=3(2)^{x}-4$ D. $f(x)=-3 x+4$

Which function has a horizontal asymptote at 4? A. $f(x)=2(3)^{x}+4$ B. $f(x)=2 x-4$ C. $f(x)=3(2)^{x}-4$ D. $f(x)=-3 x+4$

Complete the table for the function $y=-\frac{2}{3} x+7$ with domain $\{-12,-6,3,15\}$ .

Find the weight range $w$ for a healthy BMI (19-25) at heights: (a) 75 in., (b) 74 in., (c) 78 in. Round to nearest lb.

Solve the equation $C=\pi d$ for $d$ . What is $d$ in terms of $C$ ?

Find the weight range $w$ for a healthy BMI (19-25) using $\mathrm{BMI}=\frac{704 \times \text{weight}}{\text{height}^2}$ for heights: 75 in, 74 in, 78 in.

Find the production level $x$ where revenue $R=26x$ is less than cost $C=91,000+19x$ . What is $x$ ?

Find the production level $x$ where revenue $R=29x$ is less than cost $C=90,000+19x$ . When does R < C?

Find the weight range $w$ (to nearest pound) for a healthful BMI (19-25) using $BMI=\frac{704 \times(\text{weight})}{(\text{height})^2}$ . Heights: (a) 66 in, (b) 78 in, (c) 73 in.

Determine the other trigonometric functions for $\theta$ given that $\tan \theta=-\frac{1}{6}$ and $\sin \theta>0$ .

Find the exact value of $\tan \left(-\frac{\pi}{3}\right)$ using reference angles.

Find the exact value of $\sin \left(-300^{\circ}\right)$ using reference angles.

Find the exact value of $\cos \left(-\frac{\pi}{3}\right)$ using reference angles.

Find the derivative of $y=\frac{1}{x}$ , calculate $\lim_{x \to \infty} \frac{-4x}{7x-3}$ , and find two numbers with a difference of 4 that minimize their product.

Create a table and graph for $g(x)=\frac{2}{x}$ , then describe the graph in detail.

Find the average rate of change of $f(x)=\sin x$ from $x_{1}=\frac{\pi}{4}$ to $x_{2}=\frac{3\pi}{2}$ .

Find the limit of $\frac{f(x+h)-f(x)}{h}$ for $f(x)=x^{2}+1$ as $h \neq 0$ .

Differentiate the following using the Product Rule:
1. $y=x^{2}(x+1)$
2. $y=(x^{2}+3)(x+6)$
3. $y=\sqrt{x}(x^{3}+6)$
4. $y=(2 x^{2}+4 x-3)(3 x+4)$

Bestimmen Sie die Hochpunkt-Koordinaten der Funktion $f(x)=x^{4}-\frac{4}{3} x^{3}-4 x^{2}$ .