8.8_hw.pdf - Section 8.8 HW Problems Math Lab may help 1 For what values of K is the following integral improper Z K 4x dx 2 0 x 19x 90 2 Determine

8.8_hw.pdf - Section 8.8 HW Problems Math Lab may help 1...

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Section 8.8 HW Problems Math Lab may help! 1. For what values ofKis the following integral improper? 2. Determine whether the improper integral diverges or converges. If it converges, find its value.Zdyy2+ 2y-3Z -23.Comparison Test for Improper IntegralIn some cases, it is impossible to find the exact value of an improper integral but it is important todetermine whether the integral converges or diverges.Suppose the functionsfandgare continuous and 0g(x)f(x) on the interval [a,).IfRaf(x)dxconverges, thenRag(x)dxalso convergesIfRag(x)dxdiverges, thenRaf(x)dxalso diverges.This is known as the Comparison Test for improper integrals.Use the Comparison Test to determine ifZe-x2dxconverges or diverges.(Hint:Use the fact thate-x2e-xforx1)a) 1Z Use the Comparison Test to determine ifx5+ 1dxconverges or diverges.b) 1 1 (Hint:Use the fact that1x5+ 11 x5forx1) Use the Comparison Test to determine if1c)Use the Comparison Test to determine ifZπsin2xxdxconverges or diverges.d)(For more practice problems, see the textbook.) Z1 + sin2xxdxconverges or diverges.

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