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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.