作业帮((3x+1)/(3+x))^(1/(x-1)) 当x趋向于1时的极限
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((3x+1)/(3+x))^(1/(x-1)) 当x趋向于1时的极限
((3x+1)/(3+x))^(1/(x-1)) 当x趋向于1时的极限
((3x+1)/(3+x))^(1/(x-1)) 当x趋向于1时的极限
设 f(x) = ((3x+1)/(3+x))^(1/(x-1))
ln f(x) = 1/(x-1) * ln[(3x+1) /(x+3) ] = 1/(x-1) * ln[ 1+ 2(x-1) /(x+3) ]
当x->1 时,2(x-1) /(x+3) ->0,ln[ 1+ 2(x-1) /(x+3) ] 2(x-1) /(x+3)
lim(x->1) lnf(x)
= lim(x->1) [2(x-1) /(x+3)] /(x-1) 等价无穷小代换
= lim(x->1) 2/(x+3) = 1/2
原式 = e^(1/2) = √e
e^(-2)
((3x+1)/(3+x))^(1/(x-1)) =e^(ln((3x+1)/(3+x))/(x-1));
运用罗比达法则，e的指数部分为{(3+x)/(3x+1)}*{(3x+1)-3*(x+3)}/(x+3)^2,消去了（x-1）项，
把x=1代入得到指数部分为-2
所以为e^(-2)
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/X-3/-/X-1/
(3x/x-1)
x-3(x-1)
| X+1 |>| X-3 |
x+3/x-1
(x +1)(x-3)
(x+3)(x-1)
|x+1|-|x-3|
(x+1)(x-3)
x+2/x+1-x+3/x+2-x+4/x+3+x+5/x+4
[x（x+1）+x平方（x-1)]+（-3x)
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x^5-x^4+x^3-x^2+x-1
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(X+1)X(X+2)X(X+3)=504