高数极限3道题1题limx→正无穷（1 - 2/3x）^4x+12题limx→正无穷（x/1+x）^

高数极限3道题1题limx→正无穷（1 - 2/3x）^4x+12题limx→正无穷（x/1+x）^

1题.原式=lim(x->+∞){[1-2/(3x)]^(4x+1)}=lim(x->+∞){[1+(-2)/(3x)]^[(3x)/(-2)]}^[(-2)(4x+1)/(3x)]}=e^{lim(x->+∞){[(-2)(4x+1)/(3x)]} (利用特殊极限)=e^（-8/3）2题.原式=lim(x->+∞){[1+(-1)/(1+x)]^(-2x+1)}=lim(x->+∞){[1+(-1)/(1+x)]^[(1+x)/(-1)]}^[(2x-1)/(1+x)]=e^{lim(x->+∞)[(2x-1)/(1+x)]} (利用特殊极限)=e^23题.原式=lim(x->+∞){[(x+1)/(x-1)]^x}=lim(x->+∞){[1+2/(x-1)]^[(x-1)/2]}^[2x/(x-1)]=e^{lim(x->+∞)[2x/(x-1)]} (利用特殊极限)=e^2 注：利用特殊极限lim(x->+∞)[(1+1/x)^x]=1======以下答案可供参考======供参考答案1:同学你给的题目叫别人怎么做啊, 第二题是（1/x+x）^(-2x+1)吧,注意该加括号的地方要加:（x+1/(x-1）)^x,（1 - 2/3x）^(4x+1), 要不然别人怎么做啊供参考答案2:1.lim（1 - 2/3x）^（4x+1）=lim(1-2/3x)^[(-3x/2)*(-2/3x)*(4x+1)]=lim[(1-2/3x)^(-3x/2)]^[-2(4x+1)/3x]lim(1-2/3x)^(-3x/2)=e，lim[-2(4x+1)/3x]=-8/3∴lim[(1-2/3x)^(-3x/2)]^[-2(4x+1)/3x]=e^(-8/3)2.lim（x/1+x）^(-2x+1)=lim[(x+1-1)/(x+1)]^(-2x+1)=lim[1-1/(x+1)]^[(-(x+1))*(-1/(x+1))*(-2x+1)]=lim{[1-1/(x+1)]^(-(x+1))}^[(2x-1)/(x+1)]lim[1-1/(x+1)]^(-(x+1))=e,lim(2x-1)/(x+1)=2∴lim{[1-1/(x+1)]^(-(x+1))}^[(2x-1)/(x+1)]=e^23.lim（x+1/x-1）^x=lim[(x-1+2)/(x-1)]^x=lim[1+2/(x-1)]^[((x-1)/2)*(2/(x-1))*x]=lim{[1+2/(x-1)]^((x-1)/2)}^[2x/(x-1)]lim[1+2/(x-1)]^((x-1)/2)=e,lim2x/(x-1)=2∴lim{[1+2/(x-1)]^((x-1)/2)}^[2x/(x-1)]=e^2

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