lim(x→0)(e^tan x-e^sin x) - 知识问答

lim(x→0)(e^tan x-e^sin x)/x^3,

2个回答

=lim e^sinx · (e^(tanx-sinx) -1)/x^3
=1×lim (e^(tanx-sinx) -1)/x^3
=lim (tanx-sinx)/x^3
=lim (sinx /x) · lim(1/cosx -1)/x²
=lim (1-/cosx)/x² /lim cosx
=lim(1/2)x²/x² /1
=1/2

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