Question 1

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

Accepted Answer

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

Question 2

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

Accepted Answer

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

Question 3

Write the first four elements of the sequence. 
-sin (n$\pi$)

Accepted Answer

A)  1, 0, -1, 0 
B)  0, 1, 0, -1 
C)  1, 1, 1, 1 
D)  0, 0, 0, 0 
A)  1, 0, -1, 0 
B)  0, 1, 0, -1 
C)  1, 1, 1, 1 
D)  0, 0, 0, 0

Question 4

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

Accepted Answer

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

Question 5

Determine if the geometric series converges or diverges. If it converges, find its sum.
-1 +   +   +   +   + . . .

Accepted Answer

A)  converges, 3 
B)  diverges 
C)  converges,   
D)  converges,   
A)  converges, 3 
B)  diverges 
C)  converges,   
D)  converges,

Question 6

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

Accepted Answer

A)  ln 9 
B)  0 
C)  does not exist 
D)  1 
A)  ln 9 
B)  0 
C)  does not exist 
D)  1

Question 7

Find the limit of the sequence if it converges; otherwise indicate divergence.
-  = 4 +

Accepted Answer

A)  4.5 
B)  4 
C)  5 
D)  Diverges 
A)  4.5 
B)  4 
C)  5 
D)  Diverges

Question 8

Solve the problem.
-Mari drops a ball from a height of 16 meters and notices that on each bounce the ball returns to about   of its previous height. About how far will ball travel before it comes to rest?

Accepted Answer

A)  112 m 
B)  37.3 m 
C)  64 m 
D)  128 m 
A)  112 m 
B)  37.3 m 
C)  64 m 
D)  128 m

Question 9

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

Accepted Answer

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

Question 10

Find a formula for the nth term of the sequence.
-7, 8, 9, 10, 11 (integers beginning with 7)

Accepted Answer

A)    = n + 6 
B)    = n + 7 
C)    = n - 7 
D)    = n + 8 
A)    = n + 6 
B)    = n + 7 
C)    = n - 7 
D)    = n + 8

Question 11

Find the sum of the series.
-

Accepted Answer

A)  65536/3 
B)  1/ 786432 
C)  262144/3 
D)  1/196608 
A)  65536/3 
B)  1/ 786432 
C)  262144/3 
D)  1/196608

Question 12

A recursion formula and the initial term(s) of a sequence are given. Write out the first five terms of the sequence.
-  = 3,   =

Accepted Answer

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

Question 13

Find the sum of the series.
-

Accepted Answer

A)  12/37 
B)  6/37 
C)  6/35 
D)  12/35 
A)  12/37 
B)  6/37 
C)  6/35 
D)  12/35

Question 14

Find the infinite sum accurate to three decimal places.
-

Accepted Answer

A)  -0.972 
B)  1.036 
C)  -1.036 
D)  0.972 
A)  -0.972 
B)  1.036 
C)  -1.036 
D)  0.972

Question 15

Find a formula for the nth term of the sequence.
-0, -1, 0, 1, 0, -1, 0, 1 (0, -1, 0, 1 repeated)

Accepted Answer

A)    = sin   
B)    = sin(n $\pi$ ) 
C)    = cos(n $\pi$ ) 
D)    = cos   
A)    = sin   
B)    = sin(n $\pi$ ) 
C)    = cos(n $\pi$ ) 
D)    = cos

Question 16

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

Accepted Answer

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

Question 17

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

Accepted Answer

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

Question 18

A recursion formula and the initial term(s) of a sequence are given. Write out the first five terms of the sequence.
-

Accepted Answer

A)  1, 4, 5, 10, 15 
B)  1, 4, 5, 9, 14 
C)  1, 1, 2, 3, 5 
D)  1, 4, 5, 6, 7 
A)  1, 4, 5, 10, 15 
B)  1, 4, 5, 9, 14 
C)  1, 1, 2, 3, 5 
D)  1, 4, 5, 6, 7

Question 19

Determine convergence or divergence of the alternating series.
-

Accepted Answer

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

Question 20

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

Accepted Answer

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

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

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

Write the first four elements of the sequence. -sin (n $\pi$ )

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

Determine if the geometric series converges or diverges. If it converges, find its sum. -1 + + + + + . . .

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

Find the limit of the sequence if it converges; otherwise indicate divergence. - = 4 +

Solve the problem. -Mari drops a ball from a height of 16 meters and notices that on each bounce the ball returns to about of its previous height. About how far will ball travel before it comes to rest?

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

Find a formula for the nth term of the sequence. -7, 8, 9, 10, 11 (integers beginning with 7)

Find the sum of the series. -

A recursion formula and the initial term(s) of a sequence are given. Write out the first five terms of the sequence. - = 3, =

Find the sum of the series. -

Find the infinite sum accurate to three decimal places. -

Find a formula for the nth term of the sequence. -0, -1, 0, 1, 0, -1, 0, 1 (0, -1, 0, 1 repeated)

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

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

A recursion formula and the initial term(s) of a sequence are given. Write out the first five terms of the sequence. -

Determine convergence or divergence of the alternating series. -

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

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

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

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

Write the first four elements of the sequence. -sin (n π\piπ )

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

Determine if the geometric series converges or diverges. If it converges, find its sum. -1 + + + + + . . .

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

Find the limit of the sequence if it converges; otherwise indicate divergence. - = 4 +

Solve the problem. -Mari drops a ball from a height of 16 meters and notices that on each bounce the ball returns to about of its previous height. About how far will ball travel before it comes to rest?

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

Find a formula for the nth term of the sequence. -7, 8, 9, 10, 11 (integers beginning with 7)

Find the sum of the series. -

A recursion formula and the initial term(s) of a sequence are given. Write out the first five terms of the sequence. - = 3, =

Find the sum of the series. -

Find the infinite sum accurate to three decimal places. -

Find a formula for the nth term of the sequence. -0, -1, 0, 1, 0, -1, 0, 1 (0, -1, 0, 1 repeated)

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

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

A recursion formula and the initial term(s) of a sequence are given. Write out the first five terms of the sequence. -

Determine convergence or divergence of the alternating series. -

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

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

Write the first four elements of the sequence. -sin (n $\pi$ )