Question 1

Find the limit.
-

Accepted Answer

A)  2 
B)  1 
C)    
D)  0 
A)  2 
B)  1 
C)    
D)  0

Question 2

Which of the graphs shows the solution of the given initial value problem?
-  = -2x, y = -2 when x = -1

Accepted Answer

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

Question 3

Find the extreme values of the function and where they occur.
-y =

Accepted Answer

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

Question 4

Solve the problem. 
-On our moon, the acceleration of gravity is 1.6 m/   . If a rock is dropped into a crevasse, how fast will it be going just before it hits bottom 45 seconds later?

Accepted Answer

A)  3240 m/sec 
B)  72 m/sec 
C)  -36 m/sec 
D)  -72 m/sec 
A)  3240 m/sec 
B)  72 m/sec 
C)  -36 m/sec 
D)  -72 m/sec

Question 5

Find the most general antiderivative.      
-  dx

Accepted Answer

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

Question 6

Choose the one alternative that best completes the statement or answers the question. 
-The positions of two particles on the s-axis are   = sin t and   with   and   in meters and t in seconds. At what time(s) in the interval 0 $\le$ t $\le$ 2$\pi$ do the particles meet?

Accepted Answer

A)  t =$\pi$sec and t = 2$\pi$ sec 
B)  t = 3/8 $\pi$ sec and t = 11/8 $\pi$ sec 
C)  t = 3/4 $\pi$ sec and t = 11/4$\pi$ sec 
D)  t = 1/2 $\pi$ sec and t = 3/2 $\pi$ sec 
A)  t =$\pi$sec and t = 2$\pi$ sec 
B)  t = 3/8 $\pi$ sec and t = 11/8 $\pi$ sec 
C)  t = 3/4 $\pi$ sec and t = 11/4$\pi$ sec 
D)  t = 1/2 $\pi$ sec and t = 3/2 $\pi$ sec

Question 7

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) = ln (x - 3), [ 4, 8]

Accepted Answer

A)  c =   + 3 
B)  c =   + 3 
C)  c =   + 3 
D)  c =   + 3 
A)  c =   + 3 
B)  c =   + 3 
C)  c =   + 3 
D)  c =   + 3

Question 8

Choose the one alternative that best completes the statement or answers the question. 
-The 9 ft wall shown here stands 30 feet from the building. Find the length of the shortest straight beam that will reach to the side of the building from the ground outside the wall.

Accepted Answer

A)  51.3 ft 
B)  53.3 ft 
C)  52.3 ft 
D)  39 ft 
A)  51.3 ft 
B)  53.3 ft 
C)  52.3 ft 
D)  39 ft

Question 9

Determine all critical points for the function.
-f(x) =   - 9   + 10

Accepted Answer

A)  x = 0 and x = 6 
B)  x = -3 and x = 3 
C)  x = 0 
D)  x = 0 and x = 3 
A)  x = 0 and x = 6 
B)  x = -3 and x = 3 
C)  x = 0 
D)  x = 0 and x = 3

Question 10

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 = 3; local maximum at x = -3 ; concave down on (0, $\infty$); concave up on (-$\infty$, 0) 
B)  Local minimum at x = 3; local maximum at x = -3 ; concave up on (0, -3) and (3, $\infty$); concave down on (-3, 3) 
C)  Local minimum at x = 3; local maximum at x = -3 ; concave up on (0, $\infty$); concave down on (-$\infty$, 0) 
D)  Local maximum at x = 3; local minimum at x = -3 ; concave up on (0, -3) and (3, $\infty$); concave down on (-3, 3) 
A)  Local minimum at x = 3; local maximum at x = -3 ; concave down on (0, $\infty$); concave up on (-$\infty$, 0) 
B)  Local minimum at x = 3; local maximum at x = -3 ; concave up on (0, -3) and (3, $\infty$); concave down on (-3, 3) 
C)  Local minimum at x = 3; local maximum at x = -3 ; concave up on (0, $\infty$); concave down on (-$\infty$, 0) 
D)  Local maximum at x = 3; local minimum at x = -3 ; concave up on (0, -3) and (3, $\infty$); concave down on (-3, 3)

Question 11

Solve the initial value problem. 
-  = 9;   (0) = -5,   (0) = 6, y(0) = 5

Accepted Answer

A)  
  
B)  
  
C)  y = 5 
D)  
  
A)  
  
B)  
  
C)  y = 5 
D)

Question 12

Find the linearization L(x) of f(x) at x = a.
-f(x) =   , a = 8

Accepted Answer

A)  L(x) = 1/12 x + 4 /3 
B)  L(x) = 1/4 x + 4 
C)  L(x) = 1/4 x + 2/3 
D)  L(x) = 1/12 x + 2/3 
A)  L(x) = 1/12 x + 4 /3 
B)  L(x) = 1/4 x + 4 
C)  L(x) = 1/4 x + 2/3 
D)  L(x) = 1/12 x + 2/3

Question 13

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

Accepted Answer

A)  $\infty$ 
B)  0 
C)  1 
D)  8/3 
A)  $\infty$ 
B)  0 
C)  1 
D)  8/3

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) =   + x - 9;   = 1

Accepted Answer

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

Question 15

Solve the initial value problem. 
-  = -   cos   $\theta$, r(0) = -5

Accepted Answer

A)  r = sin   $\theta$ - 5 
B)  r = cos  $\theta$- 6 
C)  r = -sin   $\theta$ - 5 
D)  r = -   sin   $\theta$ - 5 
A)  r = sin   $\theta$ - 5 
B)  r = cos  $\theta$- 6 
C)  r = -sin   $\theta$ - 5 
D)  r = -   sin   $\theta$ - 5

Question 16

Express the relationship between a small change in x and the corresponding change in y in the form   . 
-y = 5   - 2x - 7

Accepted Answer

A)  dy = 10x dx 
B)  dy = ( 10x - 2) dx 
C)  dy = 10x - 4 dx 
D)  dy = 10x - 7 dx 
A)  dy = 10x dx 
B)  dy = ( 10x - 2) dx 
C)  dy = 10x - 4 dx 
D)  dy = 10x - 7 dx

Question 17

Use Newton's method to approximate all the intersection points of the pair of curves. Some preliminary graphing or analysis may help in choosing good initial approximations. Round to six decimal places.
-y = ln(x + 5) and y =

Accepted Answer

A)  x $\approx$ 0.465263 
B)  x $\approx$ 1.222763 
C)  x $\approx$ 1.475263 
D)  x $\approx$ 0.722763 
A)  x $\approx$ 0.465263 
B)  x $\approx$ 1.222763 
C)  x $\approx$ 1.475263 
D)  x $\approx$ 0.722763

Question 18

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

Accepted Answer

A) True 
 B)False

Question 19

Provide an appropriate response.  
-

Accepted Answer

A)  s = a   +   t +   
B)  s =   +   
C)  s =   +   t +   
D)  s =   -   t -   
A)  s = a   +   t +   
B)  s =   +   
C)  s =   +   t +   
D)  s =   -   t -

Question 20

Find the extreme values of the function and where they occur.
-y = x3 - 12x + 2

Accepted Answer

A)  Local maximum at (0, 0). 
B)  None 
C)  Local maximum at (-2, 18), local minimum at (2, -14). 
D)  Local maximum at (2, -14), local minimum at (-2, 18). 
A)  Local maximum at (0, 0). 
B)  None 
C)  Local maximum at (-2, 18), local minimum at (2, -14). 
D)  Local maximum at (2, -14), local minimum at (-2, 18).

Find the limit. -

Which of the graphs shows the solution of the given initial value problem? - = -2x, y = -2 when x = -1

Find the extreme values of the function and where they occur. -y =

Solve the problem. -On our moon, the acceleration of gravity is 1.6 m/ . If a rock is dropped into a crevasse, how fast will it be going just before it hits bottom 45 seconds later?

Find the most general antiderivative. - dx

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) = ln (x - 3), [ 4, 8]

Choose the one alternative that best completes the statement or answers the question. -The 9 ft wall shown here stands 30 feet from the building. Find the length of the shortest straight beam that will reach to the side of the building from the ground outside the wall.

Determine all critical points for the function. -f(x) = - 9 + 10

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. -

Solve the initial value problem. - = 9; (0) = -5, (0) = 6, y(0) = 5

Find the linearization L(x) of f(x) at x = a. -f(x) = , a = 8

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

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) = + x - 9; = 1

Solve the initial value problem. - $Solve the initial value problem. - = - cos \theta , r(0) = -5$ = - $Solve the initial value problem. - = - cos \theta , r(0) = -5$ cos $Solve the initial value problem. - = - cos \theta , r(0) = -5$ $\theta$ , r(0) = -5

Express the relationship between a small change in x and the corresponding change in y in the form . -y = 5 - 2x - 7

Use Newton's method to approximate all the intersection points of the pair of curves. Some preliminary graphing or analysis may help in choosing good initial approximations. Round to six decimal places. -y = ln(x + 5) and y =

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

Provide an appropriate response. -

Find the extreme values of the function and where they occur. -y = x³ - 12x + 2

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

Find the limit. -

Which of the graphs shows the solution of the given initial value problem? - = -2x, y = -2 when x = -1

Find the extreme values of the function and where they occur. -y =

Solve the problem. -On our moon, the acceleration of gravity is 1.6 m/ . If a rock is dropped into a crevasse, how fast will it be going just before it hits bottom 45 seconds later?

Find the most general antiderivative. - dx

Choose the one alternative that best completes the statement or answers the question. -The positions of two particles on the s-axis are = sin t and with and in meters and t in seconds. At what time(s) in the interval 0 ≤\le≤ t ≤\le≤ 2 π\piπ do the particles meet?

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) = ln (x - 3), [ 4, 8]

Choose the one alternative that best completes the statement or answers the question. -The 9 ft wall shown here stands 30 feet from the building. Find the length of the shortest straight beam that will reach to the side of the building from the ground outside the wall.

Determine all critical points for the function. -f(x) = - 9 + 10

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. -

Solve the initial value problem. - = 9; (0) = -5, (0) = 6, y(0) = 5

Find the linearization L(x) of f(x) at x = a. -f(x) = , a = 8

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

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) = + x - 9; = 1

Solve the initial value problem. - = - cos θ\thetaθ , r(0) = -5

Express the relationship between a small change in x and the corresponding change in y in the form . -y = 5 - 2x - 7

Use Newton's method to approximate all the intersection points of the pair of curves. Some preliminary graphing or analysis may help in choosing good initial approximations. Round to six decimal places. -y = ln(x + 5) and y =

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

Provide an appropriate response. -

Find the extreme values of the function and where they occur. -y = x3 - 12x + 2

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. - $Solve the initial value problem. - = - cos \theta , r(0) = -5$ = - $Solve the initial value problem. - = - cos \theta , r(0) = -5$ cos $Solve the initial value problem. - = - cos \theta , r(0) = -5$ $\theta$ , r(0) = -5

Find the extreme values of the function and where they occur. -y = x³ - 12x + 2