lim x-pi (1+cos^3x)/sin^2x (without L'hospital)

Question

lim x->pi (1+cos^3x)/sin^2x (without L'hospital)

ganeshie8 · Answer

$\large  \lim \limits_{x \to \pi}  \frac{1+\cos^3x}{\sin^2x}  $

$\large  \lim \limits_{x \to \pi}  \frac{\sin^2x + \cos^2x+\cos^3x}{\sin^2x}  $

$\large  \lim \limits_{x \to \pi}  \frac{\sin^2x }{\sin^2x}  + \frac{\cos^2x+\cos^3x}{\sin^2x}  $

$\large  \lim \limits_{x \to \pi}  1  + \frac{\cos^2x(1+\cos x)}{1-\cos^2x}  $

$\large  \lim \limits_{x \to \pi}  1  + \frac{\cos^2x(1+\cos x)}{(1+\cos x)(1-\cos x)}  $

$\large  \lim \limits_{x \to \pi}  1  + \frac{\cos^2x}{(1-\cos x)}  $

ganeshie8 · Answer

take the limit..