Question 1

Determine convergence or divergence of the series.
-

Accepted Answer

A)  Diverges 
B)  Converges 
A)  Diverges 
B)  Converges

Question 2

Solve the problem.
-A company's annual revenue for the period since 2000 can be modeled by the function   where R is in millions of dollars and n = 0 corresponds to 2000. Assuming the model accurately predicts future revenue, find the year in which the revenue first exceeds $4.98 million.

Accepted Answer

A)  2011 
B)  2009 
C)  2013 
D)  2010 
A)  2011 
B)  2009 
C)  2013 
D)  2010

Question 3

Find the limit of the sequence or determine that the limit does not exist.
-  = ln( 9n + 9) - ln( 2n - 7)

Accepted Answer

A)  does not exist 
B)  ln   
C)  ln 7 
D)  ln   
A)  does not exist 
B)  ln   
C)  ln 7 
D)  ln

Question 4

Find the limit of the sequence if it converges; otherwise indicate divergence.
-  =

Accepted Answer

A)  -9 
B)    
C)    
D)  Diverges 
A)  -9 
B)    
C)    
D)  Diverges

Question 5

Use the root test to determine if the series converges or diverges.
-

Accepted Answer

A)  Converges 
B)  Diverges 
A)  Converges 
B)  Diverges

Question 6

Use the integral test to determine whether the series converges.
-

Accepted Answer

A)  converges 
B)  diverges 
A)  converges 
B)  diverges

Question 7

Solve the problem.
-A child on a swing sweeps out a distance of 16 ft on the first pass. If she is allowed to continue swinging until she stops, and if on each pass she sweeps out a distance   of the previous pass, how far does the child travel?

Accepted Answer

A)  32 ft 
B)  80 ft 
C)  48 ft 
D)  64 ft 
A)  32 ft 
B)  80 ft 
C)  48 ft 
D)  64 ft

Question 8

Find a formula for the nth term of the sequence.
-6, 8, 10, 12, 14 (every other integer starting with 6)

Accepted Answer

A)    = 2n + 5 
B)    = 2n + 4 
C)    = n + 11 
D)    = n + 10 
A)    = 2n + 5 
B)    = 2n + 4 
C)    = n + 11 
D)    = n + 10

Question 9

Solve the problem.
-A pendulum is released and swings until it stops. If it passes through an arc of 35 inches the first pass, and if on each successive pass it travels   the distance of the preceding pass, how far will it travel before stopping?

Accepted Answer

A)  140 in. 
B)  175 in. 
C)  315 in. 
D)  210 in. 
A)  140 in. 
B)  175 in. 
C)  315 in. 
D)  210 in.

Question 10

Use the Comparison Test to determine if the series converges or diverges.
-

Accepted Answer

A)  converges 
B)  diverges 
A)  converges 
B)  diverges

Question 11

Provide an appropriate response. 
-Which of the following sequences do not meet the conditions of the Integral Test?
I.   = n(sin n + 1)
II.   =  
III.   =

Accepted Answer

A)  I and III 
B)  II and III 
C)  I only 
D)  I, II, and III 
A)  I and III 
B)  II and III 
C)  I only 
D)  I, II, and III

Question 12

Find the sum of the series.
-

Accepted Answer

A)  1/2 
B)  5/3 
C)  1/3 
D)  5/2 
A)  1/2 
B)  5/3 
C)  1/3 
D)  5/2

Question 13

Find a formula for the nth term of the sequence.
--5, -4, -3, -2, -1 (integers beginning with -5)

Accepted Answer

A)    = n - 6 
B)    = n - 5 
C)    = n + 5 
D)    = n - 4 
A)    = n - 6 
B)    = n - 5 
C)    = n + 5 
D)    = n - 4

Question 14

Use the integral test to determine whether the series converges.
-

Accepted Answer

A)  converges 
B)  diverges 
A)  converges 
B)  diverges

Question 15

Find a formula for the nth partial sum of the series and use it to find the series' sum if the series converges. 
-  +   +   + ... +   + ...

Accepted Answer

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

Question 16

Find the limit of the sequence or determine that the limit does not exist.
-  =

Accepted Answer

A)    
B)  0 
C)  1 
D)  does not exist 
A)    
B)  0 
C)  1 
D)  does not exist

Question 17

Determine if the geometric series converges or diverges. If it converges, find its sum.
-  +   +   +   +   + . . .

Accepted Answer

A)  converges,   
B)  diverges 
C)  converges,   
D)  converges,   
A)  converges,   
B)  diverges 
C)  converges,   
D)  converges,

Question 18

Find the sum of the series.
-

Accepted Answer

A)  - 33/8 
B)  3/10 
C)  159/8 
D)  123/10 
A)  - 33/8 
B)  3/10 
C)  159/8 
D)  123/10

Question 19

Determine convergence or divergence of the series.
-

Accepted Answer

A)  Converges 
B)  Diverges 
A)  Converges 
B)  Diverges

Question 20

Use the Comparison Test to determine if the series converges or diverges.
-

Accepted Answer

A)  converges 
B)  diverges 
A)  converges 
B)  diverges

Determine convergence or divergence of the series. -

Solve the problem. -A company's annual revenue for the period since 2000 can be modeled by the function where R is in millions of dollars and n = 0 corresponds to 2000. Assuming the model accurately predicts future revenue, find the year in which the revenue first exceeds $4.98 million.

Find the limit of the sequence or determine that the limit does not exist. - = ln( 9n + 9) - ln( 2n - 7)

Find the limit of the sequence if it converges; otherwise indicate divergence. - =

Use the root test to determine if the series converges or diverges. -

Use the integral test to determine whether the series converges. -

Solve the problem. -A child on a swing sweeps out a distance of 16 ft on the first pass. If she is allowed to continue swinging until she stops, and if on each pass she sweeps out a distance of the previous pass, how far does the child travel?

Find a formula for the nth term of the sequence. -6, 8, 10, 12, 14 (every other integer starting with 6)

Solve the problem. -A pendulum is released and swings until it stops. If it passes through an arc of 35 inches the first pass, and if on each successive pass it travels the distance of the preceding pass, how far will it travel before stopping?

Use the Comparison Test to determine if the series converges or diverges. -

Provide an appropriate response. -Which of the following sequences do not meet the conditions of the Integral Test? I. = n(sin n + 1) II. = III. =

Find the sum of the series. -

Find a formula for the nth term of the sequence. --5, -4, -3, -2, -1 (integers beginning with -5)

Use the integral test to determine whether the series converges. -

Find a formula for the nth partial sum of the series and use it to find the series' sum if the series converges. - + + + ... + + ...

Find the limit of the sequence or determine that the limit does not exist. - =

Determine if the geometric series converges or diverges. If it converges, find its sum. - + + + + + . . .

Find the sum of the series. -

Determine convergence or divergence of the series. -

Use the Comparison Test to determine if the series converges or diverges. -

Functions

Limits

Derivatives

Applications of the Derivative

Integration

Applications of Integration

Logarithmic, Exponential, and Hyperbolic Functions

Integration Techniques

Differential Equations

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 10: Sequences and Infinite Series

Determine convergence or divergence of the series. -

Solve the problem. -A company's annual revenue for the period since 2000 can be modeled by the function where R is in millions of dollars and n = 0 corresponds to 2000. Assuming the model accurately predicts future revenue, find the year in which the revenue first exceeds $4.98 million.

Find the limit of the sequence or determine that the limit does not exist. - = ln( 9n + 9) - ln( 2n - 7)

Find the limit of the sequence if it converges; otherwise indicate divergence. - =

Use the root test to determine if the series converges or diverges. -

Use the integral test to determine whether the series converges. -

Solve the problem. -A child on a swing sweeps out a distance of 16 ft on the first pass. If she is allowed to continue swinging until she stops, and if on each pass she sweeps out a distance of the previous pass, how far does the child travel?

Find a formula for the nth term of the sequence. -6, 8, 10, 12, 14 (every other integer starting with 6)

Solve the problem. -A pendulum is released and swings until it stops. If it passes through an arc of 35 inches the first pass, and if on each successive pass it travels the distance of the preceding pass, how far will it travel before stopping?

Use the Comparison Test to determine if the series converges or diverges. -

Provide an appropriate response. -Which of the following sequences do not meet the conditions of the Integral Test? I. = n(sin n + 1) II. = III. =

Find the sum of the series. -

Find a formula for the nth term of the sequence. --5, -4, -3, -2, -1 (integers beginning with -5)

Use the integral test to determine whether the series converges. -

Find a formula for the nth partial sum of the series and use it to find the series' sum if the series converges. - + + + ... + + ...

Find the limit of the sequence or determine that the limit does not exist. - =

Determine if the geometric series converges or diverges. If it converges, find its sum. - + + + + + . . .

Find the sum of the series. -

Determine convergence or divergence of the series. -

Use the Comparison Test to determine if the series converges or diverges. -

Functions

Limits

Derivatives

Applications of the Derivative

Integration

Applications of Integration

Logarithmic, Exponential, and Hyperbolic Functions

Integration Techniques

Differential Equations

Power Series

Parametric and Polar Curves

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Calculus

Filters