lim-x-0-sin-x-tan-x-1-x-2-1-3-1-1-sin-x-1-

Question Number 97199 by bobhans last updated on 07/Jun/20

\lim_{x \to 0} \frac{\sin x - \tan x}{(\sqrt[3]{1 + x^{2}} - 1) (\sqrt{1 + \sin x} - 1)} = ?

Answered by john santu last updated on 07/Jun/20

\lim_{x \to 0} \frac{\tan (x) (\cos x - 1)}{(\sqrt[3]{1 + x^{2}} - 1) (\sqrt{1 + \sin x} - 1)} =

\lim_{x \to 0} \frac{\tan (x) (- 2 \sin^{2} (\frac{x}{2}))}{(1 + \frac{x^{2}}{3} - 1) (1 + \frac{\sin (x)}{2} - 1)} =

\lim_{x \to 0} \frac{- 2 \times \frac{1}{4} x^{3}}{\frac{1}{6} x^{3}} = - \frac{1}{2} \times \frac{6}{1} = - 3

Commented by bobhans last updated on 07/Jun/20

yesss \dots . sir

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