lim(x→0)(cosx)^(1/ln(1+x^2))

题目

lim(x→0)(cosx)^(1/ln(1+x^2))

答案

设 f(x) = (cosx)^(1/ln(1+x^2)),ln f(x) = ln(cosx) / ln(1+x^2)x→0,ln(cosx) = ln [1 + (cosx - 1] cosx - 1 - x^2 /2ln(1+x^2) x^2lim(x→0) ln(cosx) / ln(1+x^2)= lim(x→0) (-1/2) x^2 / x^2 = -1/2lim(x→0)...