lim x→无穷 （x+4/x+2）^x,求极限

gamingcs 1年前 已收到2个回答 举报
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ztnpsi 春芽

共回答了19个问题采纳率：73.7% 举报

lim(x→∞)[(x+4)/(x+2)]^x=lim(x→∞)[1+2/(x+2)]^x
=lim(x→∞)[1+2/(x+2)]^[(x+2)/2*2x/(x+2)]
={lim(x→∞)[1+2/(x+2)]^[(x+2)/2]}^[2x/(x+2)]
=e^lim(x→∞)[2x/(x+2)]
=e^lim(x→∞)[2/(1+2/x)]
=e^[2/(1+0)]
=e²

1年前

8

434434 果实

共回答了6555个问题 举报

原式=lim(x->∞) (1+ 2/(x+2))^[(x+2)/2×2x/(x+2)]
=e^lim(x->∞)2x/(x+2)
=e^[lim(x->∞)2/(1+2/x)]
=e^2

1年前

2
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