计算极限lim(x→0)[1-x^2-e^(-x^2)]/(sin2x)^4

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计算极限lim(x→0)[1-x^2-e^(-x^2)]/(sin2x)^4

计算极限lim(x→0)[1-x^2-e^(-x^2)]/(sin2x)^4
计算极限lim(x→0)[1-x^2-e^(-x^2)]/(sin2x)^4

计算极限lim(x→0)[1-x^2-e^(-x^2)]/(sin2x)^4
lim(x→0)[1-x^2-e^(-x^2)]/(sin2x)^4 (等价无穷小代换)
=lim(x→0)[1-x^2-e^(-x^2)]/(16x^4) (0/0型 ,上下求导得)
=lim(x→0)[-2x+2xe^(-x^2)]/(32x^3)
=lim(x→0)[-1+e^(-x^2)]/(16x^2) (等价无穷小代换)
=lim(x→0)(-x^2)/(16x^2)
=-1/16

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