calculate-lim-x-0-ln-cosx-1-cos-2x-

Question Number 66317 by mathmax by abdo last updated on 12/Aug/19

c a l c u l a t e {l i m}_{x \to 0} \frac{l n (c o s x)}{1 - c o s (2 x)}

Commented by kaivan.ahmadi last updated on 12/Aug/19

\equiv {l i m}_{x \to 0} \frac{l n (c o s x)}{2 x^{2}} \overset{h o p}{=} {l i m}_{x \to 0} \frac{- s i n x}{4 x c o s x} \overset{h o p}{=}

{l i m}_{x \to 0} \frac{- c o s x}{4 c o s x - 4 x s i n x} = \frac{- 1}{4}

Commented by mathmax by abdo last updated on 12/Aug/19

t h a n k s s i r .