Question 1

A particle is moving with the given data. Find the position of the particle. $v(t)=\sin t-\cos t$ , $s(0)=0$

Accepted Answer

A)  $s(t)=1-t-\sin t$ 
B)  $s(t)=1-\cos t+\sin t$ 
C)  $s(t)=1-\cos t-\sin t$ 
D)  $s(t)=\cos t-\sin t$ 
E)  $s(t)=\cos ^{2} t$ 
A)  $s(t)=1-t-\sin t$ 
B)  $s(t)=1-\cos t+\sin t$ 
C)  $s(t)=1-\cos t-\sin t$ 
D)  $s(t)=\cos t-\sin t$ 
E)  $s(t)=\cos ^{2} t$

Question 2

Identify any transitional values of $C$ at which the basic shape of the curve changes. $f(x)=x^{3}+3 c x$

Accepted Answer

A)  $c=2$ 
B)  $c=6$ 
C)  $c=4$ 
D)  $c=0$ 
A)  $c=2$ 
B)  $c=6$ 
C)  $c=4$ 
D)  $c=0$

Question 3

Sketch the graph of the function $f(x)=\frac{-3 x^{2}}{x^{2}+1}$ using the curve-sketching guidelines.

Accepted Answer

The answer of Sketch the graph of the function \(f(x)=\frac{-3...

Question 4

You are given the graph of a function f.
   
Determine the intervals where the graph of f is concave upward and where it is concave downward. Find all inflection points of f.

Accepted Answer

The answer of You are given the graph of a...

Question 5

Find the absolute maximum and absolute minimum values, if any, of the function $f(x)=5+9 \sin 2 x$ on $\left[0, \frac{\pi}{2}\right]$ .

Accepted Answer

A)  Abs. max. $f\left(\frac{\pi}{2}\right)=14$
Abs) min. $f(0)=5$ 
B)  Abs. max. $f\left(\frac{\pi}{6}\right)=9$
Abs) min. $f(0)=f\left(\frac{\pi}{2}\right)=5$ 
C)  Abs. max. $f\left(\frac{\pi}{4}\right)=14$
Abs) min. $f(0)=f\left(\frac{\pi}{2}\right)=5$ 
D)  Abs. max. $f\left(\frac{\pi}{3}\right)=9$
Abs) min. $f(0)=5$ 
A)  Abs. max. $f\left(\frac{\pi}{2}\right)=14$
Abs) min. $f(0)=5$ 
B)  Abs. max. $f\left(\frac{\pi}{6}\right)=9$
Abs) min. $f(0)=f\left(\frac{\pi}{2}\right)=5$ 
C)  Abs. max. $f\left(\frac{\pi}{4}\right)=14$
Abs) min. $f(0)=f\left(\frac{\pi}{2}\right)=5$ 
D)  Abs. max. $f\left(\frac{\pi}{3}\right)=9$
Abs) min. $f(0)=5$

Question 6

Find the critical number(s), if any of the function $f(t)=2 t^{\frac{3}{4}}-4 t^{\frac{1}{4}}$

Accepted Answer

A)  $\frac{4}{9}$ 
B)  0, $\frac{4}{9}$ 
C)  $\frac{2}{3}$ 
D)  0, $\frac{2}{3}$ 
A)  $\frac{4}{9}$ 
B)  0, $\frac{4}{9}$ 
C)  $\frac{2}{3}$ 
D)  0, $\frac{2}{3}$

Question 7

Use Newton's method to find the zero of $f(x)=-x^{3}-3 x+1$ to within 0.00001 by solving the equation $f(x)=0$ using $x_{0}=1 \text {. }$

Accepted Answer

The answer of Use Newton's method to find the zero...

Question 8

The function $f(x)=2 x^{2}-x+6$ satisfies the hypotheses of the Mean Value Theorem on the interval $[-9,-5]$ . Find all values of c that satisfy the conclusion of the theorem.

Accepted Answer

A)  -8, -6 
B)  -8, -7 
C)  -7 
D)  -6 
A)  -8, -6 
B)  -8, -7 
C)  -7 
D)  -6

Question 9

A car braked with a constant deceleration of 40 $\mathrm{ft} / \mathrm{sec}^{2}$ , producing skid marks measuring 60 ft before coming to a stop. How fast was the car traveling when the brakes were first applied?

Accepted Answer

The answer of A car braked with a constant deceleration...

Question 10

Find the absolute minimum value(s) of $y=2 x^{2}-20 x+9$ on the interval [0, 6].

Accepted Answer

The answer of Find the absolute minimum value(s) of \(y=2...

Question 11

Evaluate the limit using l'Hôpital's Rule. $\lim _{x \rightarrow \infty} \frac{(\ln x)^{3}}{4 x^{2}}$

Accepted Answer

A)  3 
B)  $\frac{3}{8}$ 
C)  $\frac{1}{4}$ 
D)  0 
A)  3 
B)  $\frac{3}{8}$ 
C)  $\frac{1}{4}$ 
D)  0

Question 12

The function $f(x)=x \sqrt{64-x^{2}}$ satisfies the hypotheses of Rolle's Theorem on the interval $[-8,8]$ . Find all values of c that satisfy the conclusion of the theorem.

Accepted Answer

A)  $\pm 4 \sqrt{2}$ 
B)  1 
C)  $\pm 1$ 
D)  $4 \sqrt{2}$ 
A)  $\pm 4 \sqrt{2}$ 
B)  1 
C)  $\pm 1$ 
D)  $4 \sqrt{2}$

Question 13

A steel pipe is being carried down a hallway 14 ft wide. At the end of the hall there is a right-angled turn into a narrower hallway 6 ft wide. What is the length of the longest pipe that can be carried horizontally around the corner?

Accepted Answer

The answer of A steel pipe is being carried down...

Question 14

Find the absolute maximum value of y = $\sqrt{36-x^{2}}$ on the interval $[-9,9]$ .

Accepted Answer

The answer of Find the absolute maximum value of y...

Question 15

Sketch the graph of $f(x)=3 \sin t$ on $\left(0, \frac{3 \pi}{2}\right)$ and find its absolute maximum and absolute minimum values, if any.

Accepted Answer

@#IMG-DLM&
Abs. max.

Question 16

What is the function of the graph?

Accepted Answer

A)  $y=5 x^{4}-5 x^{2}+8 x+3$ 
B)  $y=x^{6}-8 x^{2}+5 x$ 
C)  $y=6 x^{3}-8 x^{2}+5$ 
D)  $y=x^{7}-8 x^{3}+5 x$ 
E)  $y=6 x^{4}-8 x^{3}+5 x$ 
A)  $y=5 x^{4}-5 x^{2}+8 x+3$ 
B)  $y=x^{6}-8 x^{2}+5 x$ 
C)  $y=6 x^{3}-8 x^{2}+5$ 
D)  $y=x^{7}-8 x^{3}+5 x$ 
E)  $y=6 x^{4}-8 x^{3}+5 x$

Question 17

Sketch the graph of the function $f(x)=\frac{e^{5 x}+e^{-5 x}}{2}$ using the curve-sketching guidelines.

Accepted Answer

The answer of Sketch the graph of the function \(f(x)=\frac{e^{5...

Question 18

Consider the function $f(x)=x^{2} e^{-9 x}$ . (a) Find the intervals on which f is increasing or decreasing. (b) Find the relative maxima and relative minima of  f.

Accepted Answer

(a) decreasing on @#LAT-DLM&
a

Question 19

Sketch the curve. $y=\sqrt{\frac{x}{x-1}}$

Accepted Answer

A)    
B)    
C)    
A)    
B)    
C)

Question 20

Given that the graph of f passes through the point (4, 69) and that the slope of its tangent line at $(x, f(x))$ is $11 x-5$ , find f (1) .

Accepted Answer

A)  0 
B)  6 
C)  1 
D)  11 
E)  12 
A)  0 
B)  6 
C)  1 
D)  11 
E)  12

A particle is moving with the given data. Find the position of the particle. $v(t)=\sin t-\cos t$ , $s(0)=0$

Identify any transitional values of $C$ at which the basic shape of the curve changes. $f(x)=x^{3}+3 c x$

Sketch the graph of the function $f(x)=\frac{-3 x^{2}}{x^{2}+1}$ using the curve-sketching guidelines.

You are given the graph of a function f. Determine the intervals where the graph of f is concave upward and where it is concave downward. Find all inflection points of f.

Find the absolute maximum and absolute minimum values, if any, of the function $f(x)=5+9 \sin 2 x$ on $\left[0, \frac{\pi}{2}\right]$ .

Find the critical number(s), if any of the function $f(t)=2 t^{\frac{3}{4}}-4 t^{\frac{1}{4}}$

Use Newton's method to find the zero of $f(x)=-x^{3}-3 x+1$ to within 0.00001 by solving the equation $f(x)=0$ using $x_{0}=1 \text {. }$ $Use Newton's method to find the zero of f(x)=-x^{3}-3 x+1 to within 0.00001 by solving the equation f(x)=0 using x_{0}=1 \text {. }$

The function $f(x)=2 x^{2}-x+6$ satisfies the hypotheses of the Mean Value Theorem on the interval $[-9,-5]$ . Find all values of c that satisfy the conclusion of the theorem.

A car braked with a constant deceleration of 40 $\mathrm{ft} / \mathrm{sec}^{2}$ , producing skid marks measuring 60 ft before coming to a stop. How fast was the car traveling when the brakes were first applied?

Find the absolute minimum value(s) of $y=2 x^{2}-20 x+9$ on the interval [0, 6].

Evaluate the limit using l'Hôpital's Rule. $\lim _{x \rightarrow \infty} \frac{(\ln x)^{3}}{4 x^{2}}$

The function $f(x)=x \sqrt{64-x^{2}}$ satisfies the hypotheses of Rolle's Theorem on the interval $[-8,8]$ . Find all values of c that satisfy the conclusion of the theorem.

A steel pipe is being carried down a hallway 14 ft wide. At the end of the hall there is a right-angled turn into a narrower hallway 6 ft wide. What is the length of the longest pipe that can be carried horizontally around the corner?

Find the absolute maximum value of y = $\sqrt{36-x^{2}}$ on the interval $[-9,9]$ .

Sketch the graph of $f(x)=3 \sin t$ on $\left(0, \frac{3 \pi}{2}\right)$ and find its absolute maximum and absolute minimum values, if any.

What is the function of the graph?

Sketch the graph of the function $f(x)=\frac{e^{5 x}+e^{-5 x}}{2}$ using the curve-sketching guidelines.

Consider the function $f(x)=x^{2} e^{-9 x}$ . (a) Find the intervals on which f is increasing or decreasing. (b) Find the relative maxima and relative minima of f.

Sketch the curve. $y=\sqrt{\frac{x}{x-1}}$

Given that the graph of f passes through the point (4, 69) and that the slope of its tangent line at $(x, f(x))$ is $11 x-5$ , find f (1) .

Functions and Limits

Derivatives

Applications of Differentiation

Applications of Integration

Inverse Functions

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Final Exam

Filters

Exam 4: Integrals

A particle is moving with the given data. Find the position of the particle. v(t)=sin⁡t−cos⁡tv(t)=\sin t-\cos tv(t)=sint−cost , s(0)=0s(0)=0s(0)=0

Identify any transitional values of CCC at which the basic shape of the curve changes. f(x)=x3+3cxf(x)=x^{3}+3 c xf(x)=x3+3cx

Sketch the graph of the function f(x)=−3x2x2+1f(x)=\frac{-3 x^{2}}{x^{2}+1}f(x)=x2+1−3x2​ using the curve-sketching guidelines.

You are given the graph of a function f. Determine the intervals where the graph of f is concave upward and where it is concave downward. Find all inflection points of f.

Find the absolute maximum and absolute minimum values, if any, of the function f(x)=5+9sin⁡2xf(x)=5+9 \sin 2 xf(x)=5+9sin2x on [0,π2]\left[0, \frac{\pi}{2}\right][0,2π​] .

Find the critical number(s), if any of the function f(t)=2t34−4t14f(t)=2 t^{\frac{3}{4}}-4 t^{\frac{1}{4}}f(t)=2t43​−4t41​

Use Newton's method to find the zero of f(x)=−x3−3x+1f(x)=-x^{3}-3 x+1f(x)=−x3−3x+1 to within 0.00001 by solving the equation f(x)=0f(x)=0f(x)=0 using x0=1. x_{0}=1 \text {. }x0​=1.

The function f(x)=2x2−x+6f(x)=2 x^{2}-x+6f(x)=2x2−x+6 satisfies the hypotheses of the Mean Value Theorem on the interval [−9,−5][-9,-5][−9,−5] . Find all values of c that satisfy the conclusion of the theorem.

A car braked with a constant deceleration of 40 ft/sec2\mathrm{ft} / \mathrm{sec}^{2}ft/sec2 , producing skid marks measuring 60 ft before coming to a stop. How fast was the car traveling when the brakes were first applied?

Find the absolute minimum value(s) of y=2x2−20x+9y=2 x^{2}-20 x+9y=2x2−20x+9 on the interval [0, 6].

Evaluate the limit using l'Hôpital's Rule. lim⁡x→∞(ln⁡x)34x2\lim _{x \rightarrow \infty} \frac{(\ln x)^{3}}{4 x^{2}}limx→∞​4x2(lnx)3​

The function f(x)=x64−x2f(x)=x \sqrt{64-x^{2}}f(x)=x64−x2​ satisfies the hypotheses of Rolle's Theorem on the interval [−8,8][-8,8][−8,8] . Find all values of c that satisfy the conclusion of the theorem.

A steel pipe is being carried down a hallway 14 ft wide. At the end of the hall there is a right-angled turn into a narrower hallway 6 ft wide. What is the length of the longest pipe that can be carried horizontally around the corner?

Find the absolute maximum value of y = 36−x2\sqrt{36-x^{2}}36−x2​ on the interval [−9,9][-9,9][−9,9] .

Sketch the graph of f(x)=3sin⁡tf(x)=3 \sin tf(x)=3sint on (0,3π2)\left(0, \frac{3 \pi}{2}\right)(0,23π​) and find its absolute maximum and absolute minimum values, if any.

What is the function of the graph?

Sketch the graph of the function f(x)=e5x+e−5x2f(x)=\frac{e^{5 x}+e^{-5 x}}{2}f(x)=2e5x+e−5x​ using the curve-sketching guidelines.

Consider the function f(x)=x2e−9xf(x)=x^{2} e^{-9 x}f(x)=x2e−9x . (a) Find the intervals on which f is increasing or decreasing. (b) Find the relative maxima and relative minima of f.

Sketch the curve. y=xx−1y=\sqrt{\frac{x}{x-1}}y=x−1x​​

Given that the graph of f passes through the point (4, 69) and that the slope of its tangent line at (x,f(x))(x, f(x))(x,f(x)) is 11x−511 x-511x−5 , find f (1) .

Functions and Limits

Derivatives

Applications of Differentiation

Applications of Integration

Inverse Functions

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Final Exam

Filters

A particle is moving with the given data. Find the position of the particle. $v(t)=\sin t-\cos t$ , $s(0)=0$

Identify any transitional values of $C$ at which the basic shape of the curve changes. $f(x)=x^{3}+3 c x$

Sketch the graph of the function $f(x)=\frac{-3 x^{2}}{x^{2}+1}$ using the curve-sketching guidelines.

Find the absolute maximum and absolute minimum values, if any, of the function $f(x)=5+9 \sin 2 x$ on $\left[0, \frac{\pi}{2}\right]$ .

Find the critical number(s), if any of the function $f(t)=2 t^{\frac{3}{4}}-4 t^{\frac{1}{4}}$

Use Newton's method to find the zero of $f(x)=-x^{3}-3 x+1$ to within 0.00001 by solving the equation $f(x)=0$ using $x_{0}=1 \text {. }$ $Use Newton's method to find the zero of f(x)=-x^{3}-3 x+1 to within 0.00001 by solving the equation f(x)=0 using x_{0}=1 \text {. }$

The function $f(x)=2 x^{2}-x+6$ satisfies the hypotheses of the Mean Value Theorem on the interval $[-9,-5]$ . Find all values of c that satisfy the conclusion of the theorem.

A car braked with a constant deceleration of 40 $\mathrm{ft} / \mathrm{sec}^{2}$ , producing skid marks measuring 60 ft before coming to a stop. How fast was the car traveling when the brakes were first applied?

Find the absolute minimum value(s) of $y=2 x^{2}-20 x+9$ on the interval [0, 6].

Evaluate the limit using l'Hôpital's Rule. $\lim _{x \rightarrow \infty} \frac{(\ln x)^{3}}{4 x^{2}}$

The function $f(x)=x \sqrt{64-x^{2}}$ satisfies the hypotheses of Rolle's Theorem on the interval $[-8,8]$ . Find all values of c that satisfy the conclusion of the theorem.

Find the absolute maximum value of y = $\sqrt{36-x^{2}}$ on the interval $[-9,9]$ .

Sketch the graph of $f(x)=3 \sin t$ on $\left(0, \frac{3 \pi}{2}\right)$ and find its absolute maximum and absolute minimum values, if any.

Sketch the graph of the function $f(x)=\frac{e^{5 x}+e^{-5 x}}{2}$ using the curve-sketching guidelines.

Consider the function $f(x)=x^{2} e^{-9 x}$ . (a) Find the intervals on which f is increasing or decreasing. (b) Find the relative maxima and relative minima of f.

Sketch the curve. $y=\sqrt{\frac{x}{x-1}}$

Given that the graph of f passes through the point (4, 69) and that the slope of its tangent line at $(x, f(x))$ is $11 x-5$ , find f (1) .