Question #db808

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Question #db808

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Answer 1 · 2017-04-06T19:52:16

$0$ $0$

Explanation:

(x^(-4/3))/sin(1/x) = $\frac{x^{- \frac{1}{3}} \cdot x^{- 1}}{sin (\frac{1}{x})} = \frac{1}{x^{\frac{1}{3}}} \frac{\frac{1}{x}}{sin (\frac{1}{x})}$ $(x^(-1/3)*x^-1)/sin(1/x) =1/x^(1/3) (1/x)/sin(1/x)$

As $x \to \infty$ $xrarroo$ ,

$\frac{1}{x^{\frac{1}{3}}} \to 0$ $1/x^(1/3) rarr 0$ and

$\frac{1}{x} \to 0$ $1/x rarr 0$ so $\frac{\frac{1}{x}}{sin (\frac{1}{x})} = 1$ $(1/x)/sin(1/x) = 1$

Therefore,

$lim_(xrarroo)x^(-4/3)/sin(1/x) =0$

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Question #db808

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