Question

lim(f(x))^（n+m)=(limf(x))^n+ (limf(x))^m.有这个公式吗?

Answer 1

首先,g(x)=x^a是连续函数,即lim[g(x),x→a]=g(a)

所以lim[f(x)^a] = [limf(x)]^a,注意a的位置

而z^(m+n)=z^m·z^n,幂指数性质.

所以lim[f(x)^(m+n)] = [limf(x)]^(m+n) = [limf(x)]^m · [limf(x)]^n