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lim（tanx/x）^[1/（x^2）]x趋近于零怎么算啊
题目详情
lim（tanx/x）^[1/（x^2）] x趋近于零怎么算啊
▼优质解答
答案和解析
原式=lim(x->0) (1+(tanx-x)/x)^[1/x^2]
=e^[lim(x->0) (tanx-x)/x^3]
=e^[lim(x->0) (sec方x-1)/3x^2]
=e^[lim(x->0) (tan方x)/3x^2]
=e^[lim(x->0) (x^2)/3x^2]
=e^(1/3)
=e^[lim(x->0) (tanx-x)/x^3]
=e^[lim(x->0) (sec方x-1)/3x^2]
=e^[lim(x->0) (tan方x)/3x^2]
=e^[lim(x->0) (x^2)/3x^2]
=e^(1/3)
看了 lim（tanx/x）^[1...的网友还看了以下：