求x趋近于0时的极限:lim(1/(arctanx)^2-1/x^2)

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求x趋近于0时的极限:lim(1/(arctanx)^2-1/x^2)

求x趋近于0时的极限:lim(1/(arctanx)^2-1/x^2)
求x趋近于0时的极限:lim(1/(arctanx)^2-1/x^2)

求x趋近于0时的极限:lim(1/(arctanx)^2-1/x^2)
lim(1/(arctanx)^2-1/x^2)
=lim (x^2-(arctanx)^2)/(x^2arctanx^2)
0/0型用洛必达法则(先将分母上arctanx~x再用洛必达):
=lim[(2x-2arctanx(1/(1+x^2)))]/4x^3
=lim[2x-2arctanx]/4x^3
0/0型用洛必达法则
=lim[2-2/1+x^2]/12x^2
=lim(x^2/1+x^2)/6x^2
=1/6

2/3