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Chapter 7: Q 1 TF (page 630)

what is the comparison test for improper integrals?

Short Answer

Expert verified

If f(x)鈮�g(x)鈮�0on the interval [0,鈭�)then

1.if鈭�0鈭�f(x)dx converges then so does鈭�0鈭�g(x)dx converges

2.if 鈭�0鈭�g(x)dxdiverges then so does鈭�0鈭�f(x)dx diverges

Step by step solution

01

The comparison test for improper integral

If f(x)鈮�g(x)鈮�0on the interval [0,鈭�)then

1.if 鈭�0鈭�f(x)dxconverges then so does 鈭�0鈭�g(x)dxconverges

2.if鈭�0鈭�g(x)dxdiverges then so does鈭�0鈭�f(x)dxdiverges

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Most popular questions from this chapter

Improper Integrals: Determine whether the following improper integrals converge or diverge.

鈭�1鈭�1x2dx.

Prove that if 鈭�k=1鈭�akconverges to L and 鈭�k=1鈭�bkconverges to M , then the series鈭�k=1鈭�ak+bk=L+M.

The contrapositive: What is the contrapositive of the implication 鈥淚f A, then B.鈥�?

Find the contrapositives of the following implications:

If a quadrilateral is a square, then it is a rectangle.

Iflimk鈫�鈭�akbk=鈭�and鈭�k=1鈭�_____Convergesthen鈭�k=1鈭�_____(converges/diverges).

Explain why a function a(x) has to be continuous in order for us to use the integral test to analyze a series 鈭�k=1鈭�akfor convergence.
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