求lim(x→0)时(1-cos x)/(e的x次方-1)ln(1+x)

问题描述:

求lim(x→0)时(1-cos x)/(e的x次方-1)ln(1+x)

x→0,等价无穷小,e^x-1 ~ x, ln(1+x)~x.变换为lim(x→0)(1-cos x)/x^2 .倍角公式1-cosx=2*sin(x/2)^2,代换为 lim(x→0)2*sin(x/2)^2/(4*(x/2)^2) , 根据等价无穷小,sinx ~ x, 变换为 lim(x→0)2/4=1...