Calc Final

Question 1

When does the divergence test show convergence?

Answer 1

Never, cannot show divergence

Question 2

When does the divergence test show divergence?

Answer 2

If lim(a –> infinity) does not equal 0, the series divergences

Question 3

When does the geometric test show convergence?

Answer 3

When absolute value of r is less than 1

Question 4

When does the geometric test show divergence?

Answer 4

When absolute value of r is greater than or equal to 1

Question 5

When does p-series test show convergence?

Answer 5

When p is greater than 1

Question 6

When does p-series show divergence?

Answer 6

When p is less than or equal to 1

Question 7

When does integral test show convergence?

Answer 7

When the integral from 1 to infinity of f(x)dx converges

Question 8

When does integral test show divergence?

Answer 8

When the integral from 1 to infinity of f(x)dx diverges

Question 9

Condition for integral test to be applied

Answer 9

f(x) has to be positive, continuous, and decreasing for x values equal to or greater than 1

Question 10

When does direct comparison test show convergence?

Answer 10

When the series is smaller than a known convergent

Question 11

When does direct comparison test show divergence?

Answer 11

When the series is bigger than a known divergent

Question 12

What should you try to compare a series to in direct comparison?

Answer 12

P-series or geometric series

Question 13

When does limit comparison show convergence?

Answer 13

When the lim(n–>infinity) of An/Bn = L > 0 and Bn is known to be convergent

Question 14

When does limit comparison show convergence?

Answer 14

When the lim(n–>infinity) of An/Bn = L > 0 and Bn is known to be divergent

Question 15

When is LCT inconclusive?

Answer 15

When L = 0 or L = infinity

Question 16

When does alternating series test show convergence?

Answer 16

When lim(n–>infinity) of Bn = 0 and Bn+1 is less than or equal to Bn

Question 17

When does AST show divergence?

Answer 17

Doesn’t say anything about divergence; if the lim(n–>infinity) of the alternating series does not equal 0, use divergence test

Question 18

When does ratio test show convergence?

Answer 18

When lim(n–>infinity) of the absolute value of An+1 over An = L < 1

Question 19

When does ratio test show divergence?

Answer 19

When lim(n–>infinity) of the absolute value of An+1 over An = L > 1

Question 20

When is the ratio test inconclusive?

Answer 20

When L = 1

Question 21

When is the ratio test helpful?

Answer 21

With factorials and ( )^n

Question 22

When does root test show convergence?

Answer 22

When lim(n–>infinity) of square root of the absolute value of An = L < 1

Question 23

When does root test show divergence?

Answer 23

When lim(n–>infinity) of square root of the absolute value of An = L > 1

Question 24

When is root test inconclusive?

Answer 24

When L = 1

Question 25

When is the root test helpful?

Answer 25

With ( )^n

Question 26

Absolute convergence

Answer 26

If the absolute value of the series An converges, then the series An is absolutely convergent (which implies the series An also converges)

Question 27

Conditional convergence

Answer 27

If the series An converges but the absolute value of the series An diverges, then the series An is conditionally convergent

Question 28

Arctan(1)

Answer 28

pi/4

Question 29

Arctan(0)

Answer 29

0

Question 30

lim(n–>infinity) of arctan(n)

Answer 30

pi/2

Question 31

ln(1)

Answer 31

0

Question 32

ln(0)

Answer 32

-infinity