求极限lim((lnsinx/x)/x^2),x趋近于0.

Question

求极限lim((lnsinx/x)/x^2),x趋近于0.

Answer 1

等价无穷小替换和洛必达法则分子ln(sinx/x)＝ln(1+(sinx-x)/x)等价于(sinx-x)/x 原式＝lim(x→0) (sinx-x)/x^3＝lim(x→0) (cosx－1)/(3x^2)＝-1/6