求(x-tanx)/(xsin^2x)的极限
问题描述：
求(x-tanx)/(xsin^2x)的极限
lim(x趋于0)x^2e^(1/x^2) lim(x趋于0+)x^sinx
答
1、原式=limx→0 (x-tanx)/x^3 (sinx~x替换)=limx→0 (1-1/cos^2x)/3x^2=limx→0 -sin^2x/3x^2=limx→0 -x^2/3x^2=-1/3；2、原式=limx→0 e^(1/x^2)/(1/x^2)=limn→∞ e^n/n=limn→∞ e^n/1=无穷大；3、原式=limx→0...