求极限LIM(趋近与0)(cot^2 *x-1/x^2)nannan na

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求极限LIM(趋近与0)(cot^2 *x-1/x^2)nannan na
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求极限LIM(趋近与0)(cot^2 *x-1/x^2)nannan na
求极限LIM(趋近与0)(cot^2 *x-1/x^2)
nannan na

求极限LIM(趋近与0)(cot^2 *x-1/x^2)nannan na
LIM(趋近与0)(cot^2 x-1/x^2)
=lim(x^2*cos^2 x-sin^2 x)/(x^2 *sin^2 x)
= lim[(x^2+1)cos^2 x-1]/x^4
= lim[(1/2)*(x^2+1)(1+cos2x)-1]/x^4
=lim[(1/2)*(x^2+1)(1+1-(2x)^2/2!+(2x)^4/4!+O(x^4))-1]/x^4 ;将cos2x按泰勒公式展开,并计算得
=-lim(2/3)*x^4/x^4=-2/3