lim-x-0-1-1-x-2-cos-x-tan-4-x-

Question Number 143532 by bramlexs22 last updated on 15/Jun/21

\lim_{x \to 0} \frac{1 - \sqrt{1 + x^{2}} \cos x}{\tan^{4} x} = ?

Answered by mathmax by abdo last updated on 15/Jun/21

cosx \sim 1 - \frac{x^{2}}{2} and \sqrt{1 + x^{2}} \sim 1 + \frac{x^{2}}{2} \Rightarrow \sqrt{1 + x^{2}} cosx \sim (1 - \frac{x^{2}}{2}) (1 + \frac{x^{2}}{2})

= 1 - \frac{x^{4}}{4} \Rightarrow 1 - \sqrt{1 + x^{2}} cosx \sim \frac{x^{4}}{4} and \tan^{4} x \sim x^{4} \Rightarrow

\lim_{x \to 0} \frac{1 - \sqrt{1 + x^{2}} cosx}{\tan^{4} x} = \frac{1}{4}

Commented by bobhans last updated on 15/Jun/21

i t h i n k t h e a n s w e r i s \frac{1}{3}

Commented by Mathspace last updated on 15/Jun/21

s h o w y o u r w o r k s i r

Commented by bobhans last updated on 15/Jun/21

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