# 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.

• 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.

• 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.

This lesson includes 9 additional question variations for subscribers.