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Badly Behaved Limits Exercises

Example 1

Determine whether the integral converges or diverges. If the integral converges, find its value.

Example 2

Determine whether the integral converges or diverges. If the integral converges, find its value.

Example 3

Determine whether the integral converges or diverges. If the integral converges, find its value.

Example 4

Determine whether the integral converges or diverges. If the integral converges, find its value.

 for p > 1

Example 5

Determine whether the integral converges or diverges. If the integral converges, find its value.

 for p < 1

Example 6

Determine if the statement is true or false. Explain your answer.

If  converges to some finite number L, then

must converge.

Example 7

Determine if the statement is true or false. Explain your answer.

If  diverges, then

must diverge also.

Example 8

Determine if the statement is true or false. Explain your answer.

If  then

must converge.

Example 9

Determine if the statement is true or false. Explain your answer.

If  then

must diverge.

Example 10

Determine whether the integral converges or diverges. If the integral converges, find its value.

Example 11

Determine whether the integral converges or diverges. Indicate on a graph the region whose weighted area is given by the integral. If the integral converges, find its value.

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