limx--gt;0(1/x^2-1/tanx^2)x趋近与0x平方分之一减去tanx平方分之一
<p>问题：limx--gt;0(1/x^2-1/tanx^2)x趋近与0x平方分之一减去tanx平方分之一<p>答案：↓↓↓<p class="nav-title mt10" style="border-top:1px solid #ccc;padding-top: 10px;">冯业铭的回答：<div class="content-b">网友采纳 lim(x-->0)(1/x^2-1/tanx^2) =lim(x-->0)(tan^2x-x^2)/(x^2*tanx^2) =lim(x-->0)(tan^2x-x^2)/(x^4) =lim(x-->0)(sin^2x-cos^2x*x^2)/(cos^2x*x^4) =lim(x-->0)(sin^2x-cos^2x*x^2)/(x^4)(0/0) =lim(x-->0)(2sinxcosx+2cosxsinx*x^2-2cos^2x*x)/(4x^3) =lim(x-->0)(sinx+sinx*x^2-cosx*x)/(2x^3)(0/0) =lim(x-->0)(cosx+cosx*x^2+2xsinx+sinx*x-cosx)/(6x^2) =lim(x-->0)(cosx*x^2+3xsinx)/(6x^2) =lim(x-->0)(cosx*x+3sinx)/(6x)(0/0) =lim(x-->0)(-sinx*x+cosx+3cosx)/(6) =2/3
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