Question

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

Answer 1

$lim_{x to 0}sqrt[x^2]{cosx} = lim_{x to 0}e^{ frac{ln(cosx)}{x^2}} = e^{ lim_{x to 0} frac{ln(cosx)}{x^2}} = e^ {lim_{x to 0} frac{-sinx}{x} frac{1}{2cosx}} = e^{frac{-1}{2}}<u></u>$