lim x趋近0 cot(x)求xcotx

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lim x趋近0 cot(x)求xcotx
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lim x趋近0 cot(x)求xcotx
lim x趋近0 cot(x)
求xcotx

lim x趋近0 cot(x)求xcotx
lim x趋近0 xcot(x)
=lim x趋近0 xcos(x)/sinx
=lim x趋近0 cos(x)
=1

用洛必达法则求解,相当于求xcosx/sinx的极限,其中x→0,分子分母分别求导,得(cosx-xsinx)/cosx在x→0时的极限,将x=0代入可得结果为1.