求lim x趋于0 时(x-sinx)/[(e^2x-1)(1-cosx)]的详细过程.

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求limx趋于0时(x-sinx)/[(e^2x-1)(1-cosx)]的详细过程.求limx趋于0时(x-sinx)/[(e^2x-1)(1-cosx)]的详细过程.求limx趋于0时(x-sinx

求lim x趋于0 时(x-sinx)/[(e^2x-1)(1-cosx)]的详细过程.
求lim x趋于0 时(x-sinx)/[(e^2x-1)(1-cosx)]的详细过程.

求lim x趋于0 时(x-sinx)/[(e^2x-1)(1-cosx)]的详细过程.
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