limx->0 (x-xcosx) /(tanx-sinx)极限

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limx->0 (x-xcosx) /(tanx-sinx)极限
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limx->0 (x-xcosx) /(tanx-sinx)极限
limx->0 (x-xcosx) /(tanx-sinx)极限

limx->0 (x-xcosx) /(tanx-sinx)极限
limx->0 (x-xcosx) /(tanx-sinx)
=limx->0 1/2*x^3 /(tanx-sinx)(运用洛必达法则)
=limx->0 3/2*x^2 /(sec^2x-cosx)(通分)
=limx->0 3/2*x^2*cos^2x /(1--cos^3x)
=limx->0 3/2*x^2 /(1--cos^3x) (再运用洛必达法则)
=limx->0 3x /(3cos^2xsinx)
=limx->0 x /sinx
=1