# Badly Behaved Limits Exercises

### Example 1

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.

### Example 2

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.

### Example 3

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.

### Example 4

for *p* > 1

### Example 5

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.