lim x趋向于无穷 {1+[2/(1+x)]}^x

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limx趋向于无穷{1+[2/(1+x)]}^xlimx趋向于无穷{1+[2/(1+x)]}^xlimx趋向于无穷{1+[2/(1+x)]}^xlim(x→∞)(1+1/x)^x=e令2/(1+x)=

lim x趋向于无穷 {1+[2/(1+x)]}^x
lim x趋向于无穷 {1+[2/(1+x)]}^x

lim x趋向于无穷 {1+[2/(1+x)]}^x
lim(x→∞)(1+1/x)^x=e
令2/(1+x)=1/t可得x=2t-1
所以lim(x→∞){1+[2/(1+x)]}^x=lim(t→∞)(1+1/t)^(2t-1)=e^2