问题 解答题
lim
x→0
ex-e-x-2x
x-sinnx
的值.
答案

应用罗比塔法则,

lim
x→0
ex-e-x-2x
x-sinnx
=
lim
x→0
ex-e-x-2
1-ncosnx
=0.(n≠1)

当n=1时,

lim
x→0
ex-e-x-2x
x-sinnx
=
lim
x→0
ex-e-x-2
1-cosx
=
lim
x→0
ex-e-x
sinx
=
lim
x→0
ex-e-x
cosx
=2

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