极限题lim x→0(tanx-sinx)/x的三次方
问题描述:
极限题lim x→0(tanx-sinx)/x的三次方
答
用泰勒展开式:
sinx=x-x^3/6+o(x^5)……
tanx=x+x^3/3+o(x^5)……
lim x→0(tanx-sinx)/x^3=lim x→0(x+x^3/3-x+x^3/6+o(x^5))/x^3=lim x→0(x^3/2+o(x^5))/x^3=1/2