高数练习题
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原式=lim(n->0) (tan^2n-n^2)/(n^2*tan^2n)
=lim(n->0) (tan^2n-n^2)/n^4
=lim(n->0) (2tann*sec^2n-2n)/4n^3
=lim(n->0) (tann*sec^2n-n)/2n^3
=lim(n->0) (sinn-n*cos^3n)/(2n^3*cos^3n)
=lim(n->0) (sinn-n)/(2n^3)
=lim(n->0) (cosn-1)/(6n^2)
=lim(n->0) (-n^2/2)/(6n^2)
=-1/12
=lim(n->0) (tan^2n-n^2)/n^4
=lim(n->0) (2tann*sec^2n-2n)/4n^3
=lim(n->0) (tann*sec^2n-n)/2n^3
=lim(n->0) (sinn-n*cos^3n)/(2n^3*cos^3n)
=lim(n->0) (sinn-n)/(2n^3)
=lim(n->0) (cosn-1)/(6n^2)
=lim(n->0) (-n^2/2)/(6n^2)
=-1/12
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