高数求极限.x趋向于零,lim(sin^2x-x^2cos^2x)/x^2sin^2x ,高数求极限.x趋向于零,lim(sin^2x-x^2cos^2x)/x^2sin^2x ,

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高数求极限.x趋向于零,lim(sin^2x-x^2cos^2x)/x^2sin^2x ,高数求极限.x趋向于零,lim(sin^2x-x^2cos^2x)/x^2sin^2x ,

高数求极限.x趋向于零,lim(sin^2x-x^2cos^2x)/x^2sin^2x ,高数求极限.x趋向于零,lim(sin^2x-x^2cos^2x)/x^2sin^2x ,
高数求极限.x趋向于零,lim(sin^2x-x^2cos^2x)/x^2sin^2x ,
高数求极限.x趋向于零,lim(sin^2x-x^2cos^2x)/x^2sin^2x ,

高数求极限.x趋向于零,lim(sin^2x-x^2cos^2x)/x^2sin^2x ,高数求极限.x趋向于零,lim(sin^2x-x^2cos^2x)/x^2sin^2x ,
sinx=x-1/6x^3+o(x^3) 则sin^2x=x^2-1/3x^4+o(x^4)
cosx=1-x^2/2+o(x^4) cos^2x=1-x^2+o(x^4)
那么分子就是sin^2x-x^2cos^2x=x^2-1/3x^4+o(x^4)-[x^2-x^4+o(x^4)]=2/3x^4+o(x^4) 所以结果是2/3
或者sin^2x-x^2cos^2x=(sinx+xcosx)(sinx-xcosx)
那么原式=lim(x-->0)(sinx+xcosx)/x*lim(x-->0)sinx-xcosx/x^3=2limxsinx/3x^2=2/3