lim(x/x-c)^x=2 x趋于无穷

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lim(x/x-c)^x=2 x趋于无穷
lim(x/x-c)^x=2 x趋于无穷

lim(x/x-c)^x=2 x趋于无穷
化为lim(x/x-c)^{(-1)(-x)}
=lim(1-c/x)^(-x)
=lim(1-c/x)^{(-c/x)(-x/c)(-x)}
=lime^c
=e^c
由e^c=2知c=ln2
因为有一个公式e^lnx=x

lim[x→∞][x/(x-c)]^x=lim[x→∞](1/(1-c/x)^x2
设t=-c/x,x=-c/t,
lim[x→∞](1/(1-c/x)^x2 =lim[x→∞]{1/[(1+t)^(1/t)]^(-c)}
=1/e^(-c)
=e^c=2,
∴c=ln2,

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