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Quizzes

1. An "improper integral" is→another name for an indefinite integral.
2. Which of the following statements must be true? Assume f is continuous and well-behaved on (0,∞).

(I) If  then  converges.
(II) If  then  diverges.
(III) If  diverges then 
(IV) If  converges then →II and IV

3. The integral →diverges
4. If  then the integral →is a definite integral
5. Which of the following integrals must converge?→
6. The integral →diverges
7.
8. The function f ( x ) is graphed below.

The integral

→converges only if a ≥ 1

9. To determine if

converges or diverges, it would be useful to compare the integrand to→

10. Given the graph below, which of the following integrals must converge?

(I)
(II)
(III) →(I)

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