Question 1

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

Accepted Answer

A) True 
 B)False

Question 2

Find the value or values of c that satisfy the equation   =   (c) in the conclusion of the Mean Value Theorem for the function and interval.
-f(x) =   + 2x + 1, [ -3, -2]

Accepted Answer

A)  -3, -2 
B)  - 5/2, 5/2 
C)  0, - 5/2 
D)  - 5/2 
A)  -3, -2 
B)  - 5/2, 5/2 
C)  0, - 5/2 
D)  - 5/2

Question 3

Solve the problem. 
-Given the acceleration, initial velocity, and initial position of a body moving along a coordinate line at time t, find the body's position at time t. a = 20, v(0) = 15, s(0) = -11

Accepted Answer

A)  s = 20   + 15t - 11 
B)  s = 10   + 15t 
C)  s = 10   + 15t - 11 
D)  s = -10   - 15t - 11 
A)  s = 20   + 15t - 11 
B)  s = 10   + 15t 
C)  s = 10   + 15t - 11 
D)  s = -10   - 15t - 11

Question 4

Provide an appropriate response.  
-The position of an object in free fall near the surface of the plane where the acceleration due to gravity has a constant magnitude of g (length-units)/secS1U1P12 S1S1P0 is given by the equation:
    where s is the height above the earth, vS1U1B10 S1U1B0 is the initial velocity, and sS1U1B10S1U1B0  is the initial height.  Give the initial value problem for this situation.  Solve it to check its validity.  Remember the positive direction is the upward direction.

Accepted Answer

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

Question 5

Solve the problem.
-The diameter of a tree was 11 in. During the following year, the circumference increased   About how much did the tree's diameter increase? (Leave your answer in terms of  $\pi$.)

Accepted Answer

A)   $\pi$/2 in. 
B)  11/ $\pi$ in. 
C)  13/  $\pi$ in. 
D)  2/ $\pi$ in. 
A)   $\pi$/2 in. 
B)  11/ $\pi$ in. 
C)  13/  $\pi$ in. 
D)  2/ $\pi$ in.

Question 6

Solve the initial value problem. 
-

Accepted Answer

A)  v = -   +   
B)  v = csc t +   
C)  v = -   + 2 
D)  v = -   + 1 
A)  v = -   +   
B)  v = csc t +   
C)  v = -   + 2 
D)  v = -   + 1

Question 7

Choose the one alternative that best completes the statement or answers the question. 
-A rectangular sheet of perimeter 24 cm and dimensions x cm by y cm is to be rolled into a cylinder as shown in part (a) of the figure. What values of x and y give the largest volume?

Accepted Answer

A)  x = 9 cm; y = 3 cm 
B)  x = 10 cm; y = 2 cm 
C)  x = 8 cm; y = 4 cm 
D)  x = 7 cm; y = 5 cm 
A)  x = 9 cm; y = 3 cm 
B)  x = 10 cm; y = 2 cm 
C)  x = 8 cm; y = 4 cm 
D)  x = 7 cm; y = 5 cm

Question 8

Solve the initial value problem. 
-  = 7t +   t, r(-$\pi$) = 2

Accepted Answer

A)  r =     + tan t + 2 -     
B)  r =     + cot t + 2 -     
C)  r = 7   + tan t + 2 - 7   
D)  r = 7 + tan t - 5 
A)  r =     + tan t + 2 -     
B)  r =     + cot t + 2 -     
C)  r = 7   + tan t + 2 - 7   
D)  r = 7 + tan t - 5

Question 9

Solve the problem. 
-Using the following properties of a twice-differentiable function y = f(x), select a possible graph of f.

Accepted Answer

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

Question 10

Choose the one alternative that best completes the statement or answers the question. 
-Find the number of units that must be produced and sold in order to yield the maximum profit, given the following equations for revenue and cost: R   = 6x
C   = 0.001   + 1.1x + 60.

Accepted Answer

A)  2450 units 
B)  7100 units 
C)  4900 units 
D)  3550 units 
A)  2450 units 
B)  7100 units 
C)  4900 units 
D)  3550 units

Question 11

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

Question 12

Choose the one alternative that best completes the statement or answers the question. 
-Find the number of units that must be produced and sold in order to yield the maximum profit, given the following equations for revenue and cost: R(x) = 60x - 0.5  
C(x) = 6x + 7.

Accepted Answer

A)  54 units 
B)  55 units 
C)  61 units 
D)  66 units 
A)  54 units 
B)  55 units 
C)  61 units 
D)  66 units

Question 13

Solve the initial value problem. 
-  = 4 -  10x,    (0) = 8, y(0) = 2

Accepted Answer

A)  y = 2   -     + 8x + 2 
B)  y = 2   +     - 8x - 2 
C)  y = 2 
D)  y = 4   + 10   + 8x + 2 
A)  y = 2   -     + 8x + 2 
B)  y = 2   +     - 8x - 2 
C)  y = 2 
D)  y = 4   + 10   + 8x + 2

Question 14

Solve the initial value problem. 
-  = 4   , y(1) = 3

Accepted Answer

A)  y =-     -   
B)  y = 16   + 48 
C)  y = 4   - 1 
D)  y = 16   - 13 
A)  y =-     -   
B)  y = 16   + 48 
C)  y = 4   - 1 
D)  y = 16   - 13

Question 15

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

Accepted Answer

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

Question 16

Solve the problem. 
-An object is dropped from 10 ft above the surface of the moon. How long will it take the object to hit the surface of the moon if

Accepted Answer

A)  1.96 sec 
B)  3.85 sec 
C)  0.96 sec 
D)  1.39 sec 
A)  1.96 sec 
B)  3.85 sec 
C)  0.96 sec 
D)  1.39 sec

Question 17

Find the extreme values of the function and where they occur.
-y = x3 - 3x2 + 1

Accepted Answer

A)  Local maximum at (0, 1), local minimum at (2, -3). 
B)  Local minimum at (2, -3). 
C)  None 
D)  Local maximum at (0, 1). 
A)  Local maximum at (0, 1), local minimum at (2, -3). 
B)  Local minimum at (2, -3). 
C)  None 
D)  Local maximum at (0, 1).

Question 18

Determine all critical points for the function.
-f(x) =

Accepted Answer

A)  x = 0 and x = 1 
B)  x = 1 
C)  x = 1 and x = 7 
D)  x = 0, x = 1, and x = 7 
A)  x = 0 and x = 1 
B)  x = 1 
C)  x = 1 and x = 7 
D)  x = 0, x = 1, and x = 7

Question 19

Find the most general antiderivative.      
-  dx

Accepted Answer

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

Question 20

Sketch the graph and show all local extrema and inflection points.
-y = x + sin x, 0 $\le$ x $\le$ 2 $\pi$

Accepted Answer

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

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

Find the value or values of c that satisfy the equation = (c) in the conclusion of the Mean Value Theorem for the function and interval. -f(x) = + 2x + 1, [ -3, -2]

Solve the problem. -Given the acceleration, initial velocity, and initial position of a body moving along a coordinate line at time t, find the body's position at time t. a = 20, v(0) = 15, s(0) = -11

Solve the initial value problem. -

Choose the one alternative that best completes the statement or answers the question. -A rectangular sheet of perimeter 24 cm and dimensions x cm by y cm is to be rolled into a cylinder as shown in part (a) of the figure. What values of x and y give the largest volume?

Solve the initial value problem. - $Solve the initial value problem. - = 7t + t, r(- \pi ) = 2$ = 7t + $Solve the initial value problem. - = 7t + t, r(- \pi ) = 2$ t, r(- $\pi$ ) = 2

Solve the problem. -Using the following properties of a twice-differentiable function y = f(x), select a possible graph of f.

Choose the one alternative that best completes the statement or answers the question. -Find the number of units that must be produced and sold in order to yield the maximum profit, given the following equations for revenue and cost: R = 6x C = 0.001 + 1.1x + 60.

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. -

Choose the one alternative that best completes the statement or answers the question. -Find the number of units that must be produced and sold in order to yield the maximum profit, given the following equations for revenue and cost: R(x) = 60x - 0.5 C(x) = 6x + 7.

Solve the initial value problem. - = 4 - 10x, (0) = 8, y(0) = 2

Solve the initial value problem. - = 4 , y(1) = 3

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

Solve the problem. -An object is dropped from 10 ft above the surface of the moon. How long will it take the object to hit the surface of the moon if

Find the extreme values of the function and where they occur. -y = x³ - 3x² + 1

Determine all critical points for the function. -f(x) =

Find the most general antiderivative. - dx

Sketch the graph and show all local extrema and inflection points. -y = x + sin x, 0 $\le$ x $\le$ 2 $\pi$ $Sketch the graph and show all local extrema and inflection points. -y = x + sin x, 0 \le x \le 2 \pi$

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

Exam 4: Applications of the Derivative

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

Find the value or values of c that satisfy the equation = (c) in the conclusion of the Mean Value Theorem for the function and interval. -f(x) = + 2x + 1, [ -3, -2]

Solve the problem. -Given the acceleration, initial velocity, and initial position of a body moving along a coordinate line at time t, find the body's position at time t. a = 20, v(0) = 15, s(0) = -11

Solve the problem. -The diameter of a tree was 11 in. During the following year, the circumference increased About how much did the tree's diameter increase? (Leave your answer in terms of π\piπ .)

Solve the initial value problem. -

Choose the one alternative that best completes the statement or answers the question. -A rectangular sheet of perimeter 24 cm and dimensions x cm by y cm is to be rolled into a cylinder as shown in part (a) of the figure. What values of x and y give the largest volume?

Solve the initial value problem. - = 7t + t, r(- π\piπ ) = 2

Solve the problem. -Using the following properties of a twice-differentiable function y = f(x), select a possible graph of f.

Choose the one alternative that best completes the statement or answers the question. -Find the number of units that must be produced and sold in order to yield the maximum profit, given the following equations for revenue and cost: R = 6x C = 0.001 + 1.1x + 60.

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. -

Choose the one alternative that best completes the statement or answers the question. -Find the number of units that must be produced and sold in order to yield the maximum profit, given the following equations for revenue and cost: R(x) = 60x - 0.5 C(x) = 6x + 7.

Solve the initial value problem. - = 4 - 10x, (0) = 8, y(0) = 2

Solve the initial value problem. - = 4 , y(1) = 3

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

Solve the problem. -An object is dropped from 10 ft above the surface of the moon. How long will it take the object to hit the surface of the moon if

Find the extreme values of the function and where they occur. -y = x3 - 3x2 + 1

Determine all critical points for the function. -f(x) =

Find the most general antiderivative. - dx

Sketch the graph and show all local extrema and inflection points. -y = x + sin x, 0 ≤\le≤ x ≤\le≤ 2 π\piπ

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

Solve the initial value problem. - $Solve the initial value problem. - = 7t + t, r(- \pi ) = 2$ = 7t + $Solve the initial value problem. - = 7t + t, r(- \pi ) = 2$ t, r(- $\pi$ ) = 2

Find the extreme values of the function and where they occur. -y = x³ - 3x² + 1

Sketch the graph and show all local extrema and inflection points. -y = x + sin x, 0 $\le$ x $\le$ 2 $\pi$ $Sketch the graph and show all local extrema and inflection points. -y = x + sin x, 0 \le x \le 2 \pi$