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anonymous
 5 years ago
convergence test
(cos x)/(x^2sin x) dx limits 1 to infinity
anonymous
 5 years ago
convergence test (cos x)/(x^2sin x) dx limits 1 to infinity

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0limits 1 to infinity converge or diverge and proof (cos x)/(x^2  sin x)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The absolute value of cosine is always less than or equal to one. So you may take,\[\frac{\cos x}{x^2  \sin x} \le \frac{1}{x^2 \sin x}=\frac{1/x^2}{1\frac{\sin x}{x^2}}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\lim_{x \rightarrow \infty}\frac{\cos x}{x^2  \sin x} \le \lim_{x \rightarrow \infty}\frac{1/x^2}{1\frac{\sin x}{x^2}}\]\[=\frac{\lim_{x \rightarrow \infty}1/x^2}{\lim_{x \rightarrow \infty}1\lim_{x \rightarrow \infty}\frac{\sin x}{x^2}}=\frac{0}{10}=0\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Damn, just spotted the 'dx'. I thought you wanted to see what the limit of this thing was. Are you using the integral test?
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