Question

lim (x-2/x+2)^x+2 x→∞ 请问这题求极限是怎样解,

Answer 1

lim_{x→∞}[(x-2)/(x+2)]^(x+2)

=lim_{x→∞}[1-4/(x+2)]^(x+2)

=lim_{x→∞}[1-4/(x+2)]^[-(x+2)/4*(-4)]

=lim_{x→∞}{[1-4/(x+2)]^[-(x+2)/4]}^(-4)

=e^(-4)