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x趋近于0lim(1/x-1/sinx)求解
题目详情
x趋近于0 lim(1/x-1/sinx)求解
▼优质解答
答案和解析
lim(x->0)(1/x-1/sinx)
= lim(x->0)(sinx-x/xsinx)
= lim(x->0)(sinx-x/x^2)
洛必达
=lim(x->0)((cosx-1)/2x)
=lim(x->0)-1/2x^2/2x
=lim(x->0)-1/4x
=0
= lim(x->0)(sinx-x/xsinx)
= lim(x->0)(sinx-x/x^2)
洛必达
=lim(x->0)((cosx-1)/2x)
=lim(x->0)-1/2x^2/2x
=lim(x->0)-1/4x
=0
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