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lim(x->0)sinx-x/tanx^3=?
题目详情
lim(x->0)sinx-x/tanx^3=?
▼优质解答
答案和解析
lim(x->0)(sinx-x)/tanx^3
=lim(x->0)[(sinx-x)/x^3][x^3/tanx^3]
=lim(x->0)[(sinx-x)/x^3]lim(x->0)[x^3/tanx^3]
=lim(x->0)[(sinx-x)/x^3]
=lim(x->0)[(cosx-1)/(3x^2)]
=lim(x->0)[(-sinx)/(6x)]
=-1/6
=lim(x->0)[(sinx-x)/x^3][x^3/tanx^3]
=lim(x->0)[(sinx-x)/x^3]lim(x->0)[x^3/tanx^3]
=lim(x->0)[(sinx-x)/x^3]
=lim(x->0)[(cosx-1)/(3x^2)]
=lim(x->0)[(-sinx)/(6x)]
=-1/6
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