X → infinity, find the limit of (x + 1) / (X-2) to the x power, whether it is the third power of E

X → infinity, find the limit of (x + 1) / (X-2) to the x power, whether it is the third power of E

lim(x→∞) [(x+1)/(x-2)]^x
=lim(x→∞) [1+3/(x-2)]^x
=lim(x→∞) [1+3/(x-2)]^{[(x-2)/3]*[3x/(x-2)]}
=lim(x→∞) e^[3x/(x-2)]
=e³