lim-x-0-sin-x-arcsin-x-

Question Number 222 by 123456 last updated on 25/Jan/15

\lim_{x \to 0} \frac{\sin x}{\arcsin x}

Answered by ghosea last updated on 16/Dec/14

\lim_{x \to 0} \frac{\sin x}{\arcsin x}

= \lim_{x \to 0} \frac{\sin x}{x} \cdot \frac{x}{\arcsin x}

= \lim_{x \to 0} \frac{\sin x}{x} \cdot \lim_{x \to 0} \frac{x}{\arcsin x}

= 1 \cdot 1 = 1

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