求极限lin(x→-∞)2x+3/x+2
\u8ba1\u7b97\u6781\u9650lin\u4e0bx\u21923=sin(x-3)/x\u5e73\u65b9-2x-3x\u21923\u5219x-3\u21920
sin\uff08x-3\uff09~x-3
lim\u4e0bx\u21923 sin(x-3)/\uff08x^2-2x-3\uff09
=limx\u21923 \uff08x-3\uff09/\uff08x-3\uff09\uff08x+1\uff09
=limx\u21923 1/\uff08x+1\uff09
=1/4
(2x-1)/(2x+1)
=1-2/(2x+1)
\u4ee41/a=-2/(2x+1)
2x+1=-2a
x=(-2a-1)/2
\u6240\u4ee5x+3/2=-a+1
x\u8d8b\u4e8e\u65e0\u7a77\u5219a\u8d8b\u4e8e\u65e0\u7a77
\u6240\u4ee5\u539f\u5f0f=lim(1+1/a)^(-a+1)
=(1+1/a)^(-a)*(1+1/a)
=[1/(1+1/a)^a]*(1+1/a)
(1+1/a)^a\u6781\u9650\u662fe\uff0c1+1/a\u8d8b\u4e8e1
\u6240\u4ee5\u6781\u9650=1/e
=limx→-∞(2+3/x)/(1+2/x)
=(2+0)/(1+0)
=2;
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