Lim(cosx)^(1/(x^2)) при xстремящемся к 0

Question

Lim(cosx)^(1/(x^2)) при xстремящемся к 0

Answer 1

" alt=" \lim_{x \to 0}\sqrt[x^2]{cosx} = \lim_{x \to 0}e^{ \frac{ln(cosx)}{x^2}} = e^{ \lim_{x \to 0} \frac{ln(cosx)}{x^2}} = e^ {\lim_{x \to 0} \frac{-sinx}{x} \frac{1}{2cosx}} = e^{\frac{-1}{2}}" align="absmiddle" class="latex-formula">