lim-x-0-sin-x-1-x-

Question Number 91020 by jagoll last updated on 27/Apr/20

\lim_{x \to 0} {(\sin x)}^{\frac{1}{x}} ?

Commented by jagoll last updated on 28/Apr/20

i t d o e s m e a n \lim_{x \to 0} {(\sin x)}^{\frac{1}{x}} D N E ?

Commented by mathmax by abdo last updated on 27/Apr/20

l e t f (x) = {(s i n x)}^{\frac{1}{x}} \Rightarrow f (x) = e^{\frac{1}{x} l n (s i n x)}

\frac{l n (s i n x)}{x} \sim \frac{l n (x)}{x} \to - \infty (x \to 0^{+}) \Rightarrow {l i m}_{x \to 0^{+}} f (x) = 0