求lim(x-0)sinx-x/xsinx的极限
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求lim(x-0)sinx-x/xsinx的极限求lim(x-0)sinx-x/xsinx的极限求lim(x-0)sinx-x/xsinx的极限lim(x-0)sinx-x/xsinxL''Hospit
求lim(x-0)sinx-x/xsinx的极限
求lim(x-0)sinx-x/xsinx的极限
求lim(x-0)sinx-x/xsinx的极限
lim(x-0)sinx-x/xsinx
L'Hospital(0/0形)
=lim(x-0)cosx-1/(sinx+xcosx)
L'Hospital(0/0形)
=lim(x-0)-sinx/(cosx+cosx-xsinx)
分子极限0 分母极限2
=0
0
0
用两次落必达法则
由泰勒定理sinx=x-x^3/6+o(x^3),知
sinx~x
sinx-x~-x^3/6
所以lim(x-0)sinx-x/xsinx=lim(x-0)-x^3/6x^2
=lim(x-0)-x/6=0
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