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lim(cot(x)(1/sin(x)-1/x))=?当x->0时急.先谢
题目详情
lim(cot(x)(1/sin(x)-1/x))=?当x->0时
急.先谢
急.先谢
▼优质解答
答案和解析
cot(x)(1/sin(x)-1/x)
=(cosx/sinx)((x-sinx)/xsinx)
=(1-xx/2)(x-sinx)/xsinxsinx
=(x-sinx-xxx/2+xxsinx/2)/xsinxsinx
=(x/sinx-1-xx/2+xx/2)/xsinx
=0/xsinx
=0
=(cosx/sinx)((x-sinx)/xsinx)
=(1-xx/2)(x-sinx)/xsinxsinx
=(x-sinx-xxx/2+xxsinx/2)/xsinxsinx
=(x/sinx-1-xx/2+xx/2)/xsinx
=0/xsinx
=0
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