find-lim-x-0-x-sinx-x-sinx-

Question Number 176388 by Matica last updated on 18/Sep/22

f i n d \lim_{x \to 0} \frac{x + s i n x}{x - s i n x}

Commented by Matica last updated on 18/Sep/22

\underset{x \to 0}{l i m} \frac{x + s i n x}{x - s i n x} \overset{?}{=} - \infty

Answered by cortano1 last updated on 18/Sep/22

\lim_{x \to 0} \frac{1 + \cos x}{1 - \cos x} = \lim_{x \to 0} \frac{{(1 + \cos x)}^{2}}{\sin^{2} x}

= 4 . {[\lim_{x \to 0} \frac{1}{\sin x}]}^{2} = 4 (\infty) = \infty

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