Question 1

Solve the initial value problem. 
-  = cos t - sin t, s   = 7

Accepted Answer

A)  s = 2sin t + 5 
B)  s = sin t - cos t + 6 
C)  s = sin t + cos t + 8 
D)  s = sin t + cos t + 6 
A)  s = 2sin t + 5 
B)  s = sin t - cos t + 6 
C)  s = sin t + cos t + 8 
D)  s = sin t + cos t + 6 D

Question 2

Find all the roots of the function. Use preliminary analysis and graphing to determine good initial approximations. Round to six decimal places.
-f(x) = ln( 2x) - 2   + 3x + 1

Accepted Answer

A)  x $\approx$ 0.128994, 2.082514 
B)  x$\approx$ 0.351105, 2.304625 
C)  x$\approx$0.129105, 2.082625 
D)  x $\approx$ 1.629105, 3.582625 
A)  x $\approx$ 0.128994, 2.082514 
B)  x$\approx$ 0.351105, 2.304625 
C)  x$\approx$0.129105, 2.082625 
D)  x $\approx$ 1.629105, 3.582625 C

Question 3

Find the limit.
-

Accepted Answer

A)  4.5 
B)    
C)  $\infty$ 
D)  0 
E)  1 
A)  4.5 
B)    
C)  $\infty$ 
D)  0 
E)  1 B

Question 4

Find the most general antiderivative.      
-  dt

Accepted Answer

A)  
  
B)  
  
C)  -2 cos t + C 
D)  -2sin t + C 
A)  
  
B)  
  
C)  -2 cos t + C 
D)  -2sin t + C

Question 5

Determine all critical points for the function.
-y = 3   - 96

Accepted Answer

A)  x = 4 
B)  x = 0 and x = 4 
C)  x = 0, x = 4, and x = -4 
D)  x = 0 
A)  x = 4 
B)  x = 0 and x = 4 
C)  x = 0, x = 4, and x = -4 
D)  x = 0

Question 6

L'Hopital's rule does not help with the given limit. Find the limit some other way.
-

Accepted Answer

A)  -1 
B)  $\infty$ 
C)  1 
D)  0 
A)  -1 
B)  $\infty$ 
C)  1 
D)  0

Question 7

Use differentiation to determine whether the integral formula is correct.
-

Accepted Answer

A) True 
 B)False

Question 8

Determine whether the function satisfies the hypotheses of the Mean Value Theorem for the given interval.
-s(t) =   ,

Accepted Answer

A) True 
 B)False

Question 9

Solve the problem. 
-You are driving along a highway at a steady 85 ft/sec when you see a deer ahead and slam on the brakes. What constant deceleration is required to stop your car in

Accepted Answer

A)  17.71 ft/   
B)  0.06 ft/   
C)  35.42 ft/   
D)  8.85 ft/   
A)  17.71 ft/   
B)  0.06 ft/   
C)  35.42 ft/   
D)  8.85 ft/

Question 10

Use l'Hopital's Rule to evaluate the limit.
-

Accepted Answer

A) $\infty$ 
B)  0 
C)  1 
D)  -1 
A) $\infty$ 
B)  0 
C)  1 
D)  -1

Question 11

Find the most general antiderivative.      
-  dt

Accepted Answer

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

Question 12

A fixed point of f is a value of x that satisfies the equation f(x) = x; it corresponds to a point at which the graph of f intersects the line y = x. Find all the fixed points of the function. Use preliminary analysis and graphing to determine good initial approximations. Round approximations to six decimal places.
-f(x) =   - 5

Accepted Answer

A) x $\approx$ -2.291288, 2.291288 
B)  x $\approx$ -1.791288, 2.791288 
C)  x $\approx$ -2.791288, 3.791288 
D)  x $\approx$ -1.291288, 2.291288 
A) x $\approx$ -2.291288, 2.291288 
B)  x $\approx$ -1.791288, 2.791288 
C)  x $\approx$ -2.791288, 3.791288 
D)  x $\approx$ -1.291288, 2.291288

Question 13

Find the largest open interval where the function is changing as requested.
-Decreasing f(x) = x3 - 4x

Accepted Answer

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

Question 14

Use a calculator to compute the first 10 iterations of Newton's method when applied to the function with the given initial approximation. Make a table for the values. Round to six decimal places.
-f(x) = 3x - cos x;   = 1

Accepted Answer

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

Question 15

Express the relationship between a small change in x and the corresponding change in y in the form   . 
-y =

Accepted Answer

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

Question 16

Use the graph of the function f(x) to locate the local extrema and identify the intervals where the function is concave up and concave down.   
-

Accepted Answer

A)  Local minimum at x = 1; local maximum at x = -1; concave down on (0, $\infty$); concave up on (-$\infty$, 0) 
B)  Local minimum at x = 1; local maximum at x = -1; concave up on (0,$\infty$); concave down on (-$\infty$, 0) 
C)  Local minimum at x = 1; local maximum at x = -1; concave down on (-$\infty$, $\infty$) 
D)  Local minimum at x = 1; local maximum at x = -1; concave up on (-$\infty$, $\infty$) 
A)  Local minimum at x = 1; local maximum at x = -1; concave down on (0, $\infty$); concave up on (-$\infty$, 0) 
B)  Local minimum at x = 1; local maximum at x = -1; concave up on (0,$\infty$); concave down on (-$\infty$, 0) 
C)  Local minimum at x = 1; local maximum at x = -1; concave down on (-$\infty$, $\infty$) 
D)  Local minimum at x = 1; local maximum at x = -1; concave up on (-$\infty$, $\infty$)

Question 17

For the given expression   , find y'' and sketch the general shape of the graph of y = f(x).
-  =   ( 1 - x)

Accepted Answer

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

Question 18

Choose the one alternative that best completes the statement or answers the question. 
-Determine the dimensions of the rectangle of largest area that can be inscribed in a semicircle of radius 3.

Accepted Answer

A)  h =   , w = 3   
B)  h = 3   , w = ,   
C)  h =   , w = 3   
D)  h = 3   , w =   
A)  h =   , w = 3   
B)  h = 3   , w = ,   
C)  h =   , w = 3   
D)  h = 3   , w =

Question 19

Find the absolute extreme values of the function on the interval.
-f(x) = tan x, -   $\le$ x$\le$

Accepted Answer

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

Question 20

Find the most general antiderivative.      
-  dx

Accepted Answer

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

Solve the initial value problem. - = cos t - sin t, s = 7

Find all the roots of the function. Use preliminary analysis and graphing to determine good initial approximations. Round to six decimal places. -f(x) = ln( 2x) - 2 + 3x + 1

Find the limit. -

Find the most general antiderivative. - dt

Determine all critical points for the function. -y = 3 - 96

L'Hopital's rule does not help with the given limit. Find the limit some other way. -

Use differentiation to determine whether the integral formula is correct. -

Determine whether the function satisfies the hypotheses of the Mean Value Theorem for the given interval. -s(t) = ,

Solve the problem. -You are driving along a highway at a steady 85 ft/sec when you see a deer ahead and slam on the brakes. What constant deceleration is required to stop your car in

Use l'Hopital's Rule to evaluate the limit. -

Find the most general antiderivative. - dt

Find the largest open interval where the function is changing as requested. -Decreasing f(x) = x³ - 4x

Use a calculator to compute the first 10 iterations of Newton's method when applied to the function with the given initial approximation. Make a table for the values. Round to six decimal places. -f(x) = 3x - cos x; = 1

Express the relationship between a small change in x and the corresponding change in y in the form . -y =

Use the graph of the function f(x) to locate the local extrema and identify the intervals where the function is concave up and concave down. -

For the given expression , find y'' and sketch the general shape of the graph of y = f(x). - = ( 1 - x)

Choose the one alternative that best completes the statement or answers the question. -Determine the dimensions of the rectangle of largest area that can be inscribed in a semicircle of radius 3.

Find the absolute extreme values of the function on the interval. -f(x) = tan x, - $Find the absolute extreme values of the function on the interval. -f(x) = tan x, - \le x \le$ $\le$ x $\le$ $Find the absolute extreme values of the function on the interval. -f(x) = tan x, - \le x \le$

Find the most general antiderivative. - dx

Functions

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Derivatives

Integration

Applications of Integration

Logarithmic, Exponential, and Hyperbolic Functions

Integration Techniques

Differential Equations

Sequences and Infinite Series

Power Series

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Vectors and the Geometry of Space

Vector-Valued Functions

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Exam 4: Applications of the Derivative

Solve the initial value problem. - = cos t - sin t, s = 7

Find all the roots of the function. Use preliminary analysis and graphing to determine good initial approximations. Round to six decimal places. -f(x) = ln( 2x) - 2 + 3x + 1

Find the limit. -

Find the most general antiderivative. - dt

Determine all critical points for the function. -y = 3 - 96

L'Hopital's rule does not help with the given limit. Find the limit some other way. -

Use differentiation to determine whether the integral formula is correct. -

Determine whether the function satisfies the hypotheses of the Mean Value Theorem for the given interval. -s(t) = ,

Solve the problem. -You are driving along a highway at a steady 85 ft/sec when you see a deer ahead and slam on the brakes. What constant deceleration is required to stop your car in

Use l'Hopital's Rule to evaluate the limit. -

Find the most general antiderivative. - dt

Find the largest open interval where the function is changing as requested. -Decreasing f(x) = x3 - 4x

Use a calculator to compute the first 10 iterations of Newton's method when applied to the function with the given initial approximation. Make a table for the values. Round to six decimal places. -f(x) = 3x - cos x; = 1

Express the relationship between a small change in x and the corresponding change in y in the form . -y =

Use the graph of the function f(x) to locate the local extrema and identify the intervals where the function is concave up and concave down. -

For the given expression , find y'' and sketch the general shape of the graph of y = f(x). - = ( 1 - x)

Choose the one alternative that best completes the statement or answers the question. -Determine the dimensions of the rectangle of largest area that can be inscribed in a semicircle of radius 3.

Find the absolute extreme values of the function on the interval. -f(x) = tan x, - ≤\le≤ x ≤\le≤

Find the most general antiderivative. - dx

Functions

Limits

Derivatives

Integration

Applications of Integration

Logarithmic, Exponential, and Hyperbolic Functions

Integration Techniques

Differential Equations

Sequences and Infinite Series

Power Series

Parametric and Polar Curves

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Calculus

Filters

Find the largest open interval where the function is changing as requested. -Decreasing f(x) = x³ - 4x

Find the absolute extreme values of the function on the interval. -f(x) = tan x, - $Find the absolute extreme values of the function on the interval. -f(x) = tan x, - \le x \le$ $\le$ x $\le$ $Find the absolute extreme values of the function on the interval. -f(x) = tan x, - \le x \le$