求lim x趋于0 时(x-sinx)/[(e^2x-1)(1-cosx)]的详细过程.
问题描述：
求lim x趋于0 时(x-sinx)/[(e^2x-1)(1-cosx)]的详细过程.
答
lim(x→0) (x-sinx)/[(e^2x-1)(1-cosx)]
=lim(x→0) (x-sinx)/(2x*x^2/2)
=lim(x→0) (x-sinx)/x^3
=lim(x→0) (1-cosx)/(3x^2)
=lim(x→0) (x^2/2)/(3x^2)
=1/6