函数求极限 lim((1/x^2)-(cotx)^2) x→0 求完整解题步骤，万分感谢

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详解斗肆如空如轿下：橡做

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lim((1/卜衡x^2)-(cotx)^2) x→0

=lim((1/x^2)-(cosx/sinx)^2) x→0
=lim(sin²x-x²cosx)/x²sin²x
=lim(sin²x-x²氏弊搏cosx)/x^4
=lim(2sinxcosx-2xcosx+x²sinx)/4x³歼祥
=lim(2cos²x-2sin²x-2cosx+2xsinx+2xsinx+x²cosx)/12x²
=lim(-2cosxsinx-4sinxcosx+2sinx+4sinx+4xcosx+2xcosx-x²sinx)/24x
=(-2-4+2+4+4+2-0)/24
=6/24
=1/4

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