求极限lim(x→0) (sinx-x)/xsinxlim(x→0) (sinx-x)/xsinx 最好详细点
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求极限lim(x→0) (sinx-x)/xsinx
lim(x→0) (sinx-x)/xsinx 最好详细点
诺必达法则(只适用于0/0或是无穷/无穷):
当x=0时,分子分母都为0,分子分母可以同时求导,求导后如下:
lim(x→0) (cosx-1)/(sinx+xcosx)
分子分母还是0/0,再求导:
lim(x→0) (sinx-0)/(cosx+cosx+xsinx)
当x为0时,上式为lim(x→0)(0-0)/(1+1+0)=0
(1-0.5派+2派)/(0.5派+K派) k属于整数
lim(x→0) (sinx-x)/xsinx
=lim(x→0) (1/x - 1/sinx)
x→0 1/x → ∞
则lim(x→0) (sinx-x)/xsinx
=∞
原式=lim(x~0)[sinx/xsinx-x/xsinx]=lim(x~0)[1/x-1/x]=0(等价无穷小x~sinx)这样很明显结果等于0
infinite
x-sinx等价无穷小1/6x^3
sinx等价无穷小x
原式=lim(-1/6x^3)/x^2=lim-1/6x=0
lim(x→0) (sinx-x)/xsinx
=lim(x→0) (1/X - 1/sinx)
=0
个人认为以上答案的过程都有问题!!!
lim(x→0) (sinx-x)/xsinx =lim(x→0) (sinx/x-1)/sinx =lim(x→0)1/sinx*(sinx/x-1)
因为lim(x→0)sinx/x=1,所以lim(x→0)(sinx/x-1)=0,所以原式=0
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