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lim_x->0 f(x)/(1-cosx)
=lim_x->0 [f(x)/x^2]*[x^2/(1-cosx)]
=lim_x->0 [f(x)/x^2]* lim_x->0 [x^2/(1-cosx)]
=2*lim_x->0 [x^2/(1-cosx)]
=2*2
=4
(因为1-cosx = x^2/2+o(x^2),所以 lim_x->0 [x^2/(1-cosx)] ＝ lim_x->0 x^2/(x^2/2) = 2.)
1年前
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