问题描述: lim根号下(1-cosx平方)/(1-cosx)=是cos(x*x),不是cosx*cosx 1个回答 分类:数学 2014-10-20 问题解答: 我来补答 lim(x->0)[√(1-cos(x²))/(1-cosx)]=lim(x->0)[√(2sin²(x²/2))/(2sin²(x/2))] (应用三角函数倍角公式)=lim(x->0)[√2sin(x²/2)/(2sin²(x/2))]=lim(x->0)[√2*(sin(x²/2)/(x²/2))*((x/2)/sin(x/2))²]=√2*lim(x->0)[sin(x²/2)/(x²/2)]*lim(x->0)[(x/2)/sin(x/2)]=√2*1*1 (应用重要极限lim(t->0)(sint/t)=1)=√2. 展开全文阅读