Question

I want its full solution ....​

Answer 1

Step-by-step explanation:

We have,

$\lim_{x \rarr0} \frac{ log(1 - {x}^{2} ) }{ log( \cos(x) ) }$

$= \lim_{x \rarr0} \frac{ \frac{d}{dx}( log(1 - {x}^{2} ) )}{ \frac{d}{dx} (log( \cos(x) ) )}$

$= \lim_{x \rarr0} \frac{ \frac{ - 2x}{1 - {x}^{2} } }{ \frac{ - \sin(x) }{ \cos(x) } }$

$= \lim_{x \rarr0} \frac{2 }{( 1 - {x}^{2}) }. \lim_{x \rarr0} \frac{x}{ \tan(x) }$

$= \frac{2}{ 1 - 0} \times 1$

$= 2$

Answer 2

Step-by-step explanation:

Excellent

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