Question

lim{[(e^x)sinx-x(x 1)]/tanxsin(x^2)}.当x趋于0时的极限

求大神解答
已解决

Answer 1

x->0
tanx. sin(x^2) ~ x^3
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e^x ~ 1+ x + (1/2)x^2 + (1/6)x^3
sinx ~ x- (1/6)x^3
e^x . sinx
~ [1+ x + (1/2)x^2 + (1/6)x^3] .[x- (1/6)x^3]
~ x+x^2 +(1/2)x^3
e^x . sinx - x(x+1) ~(1/2)x^3
-----
lim(x->0) [e^x . sinx - x(x+1)] /tanx. sin(x^2)
=lim(x->0) (1/2)x^3/(x^3)
=1/2

Answer 2

题目没看懂