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Comparing integrals Graph the functions f(x) = ±l/x2, g(x)

Chapter 1, Problem 50RE

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QUESTION:

Comparing integrals Graph the functions \(f(x)=\pm 1 / x^{2}\), \(g(x)=(\cos x) / x^{2}\), and \(h(x)=\left(\cos ^{2} x\right) / x^{2}\). Without evaluating integrals and knowing that \(\int_{1}^{\infty} f(x) d x\) they have a finite value, determine whether \(\int_{1}^{\infty} g(x) \ d x\) and \(\int_{1}^{\infty} h(x) \ d x) have finite values.

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QUESTION:

Comparing integrals Graph the functions \(f(x)=\pm 1 / x^{2}\), \(g(x)=(\cos x) / x^{2}\), and \(h(x)=\left(\cos ^{2} x\right) / x^{2}\). Without evaluating integrals and knowing that \(\int_{1}^{\infty} f(x) d x\) they have a finite value, determine whether \(\int_{1}^{\infty} g(x) \ d x\) and \(\int_{1}^{\infty} h(x) \ d x) have finite values.

ANSWER:

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Graphs of the given functions are ,

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