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# Badly Behaved Functions 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 whether each statement is true or false. Explain your answers.

If  does not exist, then

must diverge.

### Example 7

If  does not exist, then

must converge.

### Example 8

Determine whether the integral converges or diverges, and find its value if it converges.

### Example 9

Determine whether the integral converges or diverges, and find its value if it converges.