xcotx,x趋向于零,tanx-sinx/x,
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1.lim(x->0)xcotx

=lim(x->0)x/tanx

=lim(x->0)x/x

=1

2.lim(x->0)(tanx-sinx)/x

=lim(x->0)tanx(1-cosx)/x

=lim(x->0)x(x²/2)/x

=lim(x->0)x²/2

=0

(本题分母一般为x³)

3.lim(x->0)(1-cos2x)/xsinx

=lim(x->0)[(2x)²/2]/x²

=lim(x->0)2x²/x²

=2

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