Question

高数，求极限问题。

如图

Answer 1

方法辩弊斗如下，携磨
请作参卜枯考：

Answer 2

Answer 3

解:设u=e^x×cosx-1-x，v=x² 原式=lim(x-0)u/v=lim(x-0)u'/宴颤拦晌胡v'=lim(x-0)u"洞困/v" lim(x-0)(e^x×cosx-e^x×sinx-1)'/2x= -lim(x-0)e^xsinx=0

Answer 4

x->0
e^x = 1+x +(1/2)x^2+o(x^2)
cosx = 1-(1/2)^2 +o(x^2)
e^x.cosx
=[1+x +(1/雀戚做2)x^2+o(x^2)].[1-(1/2)x^2 +o(x^2)]
=[1-(1/仔橡2)x^2 +o(x^2)]+x[1-(1/2)x^2 +o(x^2)] +(1/顷衡2)x^2.[1-(1/2)x^2 +o(x^2)] +o(x^2)
=[1-(1/2)x^2 +o(x^2)]+[x+o(x^2)] +[(1/2)x^2 +o(x^2)] +o(x^2)
=1+x +o(x^2)
e^x.cosx -1-x =o(x^2)
lim(x->0) [e^x.cosx -1-x]/x^2 =0

Answer 5

这个题其实也很简单的因为这是极限题中的一种传统题目

可以孙早直正凯厅接用那个洛必达法则 也可以用泰勒公式展开来求举隐解的