This lesson includes 9 additional question variations for subscribers.
Lesson Worksheet: Comparison Test for Improper Integrals Mathematics
In this worksheet, we will practice determining whether an improper integral is convergent or divergent using the comparison test for improper integrals.
Q1:
Use the comparison theorem to determine whether the integral is convergent or divergent.
- Aconvergent
- Bdivergent
Q2:
Use the comparison theorem to determine whether the integral is convergent or divergent.
- Adivergent
- Bconvergent
Q3:
Use the comparison theorem to determine whether the integral is convergent or divergent.
- Aconvergent
- Bdivergent
Q4:
Use the comparison theorem to determine whether the integral is convergent or divergent.
- Aconvergent
- Bdivergent
Q5:
Use the comparison theorem to determine whether the integral is convergent or divergent.
- Aconvergent
- Bdivergent
Q6:
Use the comparison theorem to determine whether the integral is convergent or divergent.
- Aconvergent
- Bdivergent
Q7:
Determine whether is convergent, divergent, or cannot be determined.
- ADivergent
- BCannot be determined
- CConvergent
Q8:
For what values of is the integral convergent?
- A
- B
- C
- D
- E
Q9:
For what values of is the integral convergent?
- A
- B
- C
- D
- E
Q10:
Suppose that and are continuous and for all .
Which of the following statements is true?
- AIf is convergent, then is convergent, and if is divergent, then is divergent.
- BIf is convergent, then is convergent, and if is divergent, then is divergent.
- CIf is convergent, then is convergent, and if is divergent, then is divergent.
- DIf is convergent, then is divergent, and if is divergent, then is divergent.
- EIf is divergent, then is convergent, and if is divergent, then is divergent.