lim(x趋向于0)(1-cosx)/x^2

问题描述:

lim(x趋向于0)(1-cosx)/x^2
1个回答 分类:数学 2014-10-12

问题解答:

我来补答
倍角公式:cosx=1-2[sin(x/2)]^2
故1-cosx=2[sin(x/2)]^2
于是
lim x->0 (1-cosx)/x^2
=lim x->0 2[sin(x/2)]^2/x^2
=lim x->0 2[(sin(x/2)/(x/2)]^2*1/4
=lim x->0 1/2*[(sin(x/2)/(x/2)]^2
=1/2
 
 
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