Deck 8: Section 8: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Question 1

Determine whether the improper integral diverges or converges. Evaluate the integral if it converges.

A)
B)
C)
D)
E) diverges

Answer 1

Question 2

Determine whether the improper integral diverges or converges.

A)
B)

Answer 2

Question 3

Determine whether the improper integral diverges or converges. Evaluate the integral if it converges.

A)
B)
C)
D)
E) diverges

Answer 3

Question 4

Determine whether the improper integral diverges or converges. Evaluate the integral if it converges.

A)
B)

Question 5

Suppose the capitalized cost C is given by where is the original investment, t is the time in years, r is the annual interest rate compounded continuously, and is the annual cost of maintenance. Find the capitalized cost C of an asset forever if . Round your answer to the nearest dollar.

A)
B)
C)
D)
E)

Question 6

Determine whether the improper integral diverges or converges. Evaluate the integral if it converges.

A)
B)
C) diverges
D)
E)

Question 7

Determine whether the improper integral diverges or converges. Evaluate the integral if it converges.

A)
B)
C)
D)
E) diverges

Question 8

Find the area between the x-axis and the graph of the function .

A)
B)
C)
D)
E)

Question 9

Determine whether the improper integral diverges or converges. Evaluate the integral if it converges.

A)
B)
C)
D)
E) diverges

Question 10

Determine whether the improper integral diverges or converges.

A) converges
B) diverges

Question 11

Determine whether the improper integral diverges or converges. Evaluate the integral if it converges.

A)
B)
C)
D)
E) diverges

Question 12

Suppose the capitalized cost C is given by where is the original investment, t is the time in years, r is the annual interest rate compounded continuously, and is the annual cost of maintenance. Find the capitalized cost C of an asset forever if . Round your answer to the nearest dollar.

A) 681,400
B) 1,753,400
C) 1,799,511
D) 681,420
E)

Question 13

Determine whether the improper integral diverges or converges. Evaluate the integral if it converges.

A) 18
B) 9
C)
D) 3
E) diverges

Question 14

Determine whether the improper integral diverges or converges. Evaluate the integral if it converges.

A)
B)
C)
D)
E) diverges

Question 15

Determine whether the improper integral diverges or converges.

A)
B)