lim-x-0-ln-1-sinx-sinx-with-out-H-L-Roule-

Question Number 184878 by mathlove last updated on 13/Jan/23

\lim_{x \to 0} \frac{l n (1 + s i n x)}{s i n x} = ?

w i t h o u t H^{'} L R o u l e

Answered by aba last updated on 13/Jan/23

let t = \sin (x)

x \to 0, t \to 0

\lim_{x \to 0} \frac{\ln (1 + \sin (x))}{\sin (x)} = \lim_{t \to 0} \frac{\ln (1 + t)}{t} = 1

Commented by mathlove last updated on 13/Jan/23

t h a n k s a l o t s i r