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Question Number 205339 by depressiveshrek last updated on 17/Mar/24

$$\underset{x\to 0}{\lim }\frac{\tan \left(\tan x\right)}{\sin (1-\cos x)}$$

Answered by MM42 last updated on 18/Mar/24

$$={lim}_{x\to 0}\frac{tan\left(x\right)}{sin\left(\frac{1}{2}{x}^2\right)}$$$$={lim}_{x\to 0}\frac{x}{\frac{1}{2}{x}^2}$$$$={lim}_{x\to 0}\frac{2}{x}=\{\begin{array}{l}+\mathrm{\infty }ifx\to 0^{+}\\ -\mathrm{\infty }ifx\to 0^{-}\end{array}$$$$$$

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