limx→∞[（x+c)/(x-c)]^x=4.,则常数C=?

Question

limx→∞[（x+c)/(x-c)]^x=4.,则常数C=?

Answer 1

limx→∞[（x+c)/(x-c)]^x
=limx→∞[1+2c/(x-c)]^x(设y=(x-c)/2c)
=limx→∞(1+1/y)^(2cy+c)（因1+1/y->1)
=limx→∞[(1+1/y)^y]^2c
=e^2c=4
所以c=ln2.