Question

求极值x→∞ lim(3+x)/(x+2)^ 2x

Answer 1

lim(x→∞) [(3+x)/(x+2)]^ 2x

= lim(x→∞) [1 + 1/(x+2)]^ 2x

= lim(x→∞) {[1 + 1/(x+2)]^ (x+2)}^ [2x/(x+2)]

= lim(x→∞) e^ [2x/(x+2)]

= lim(x→∞) e^ [2 - 4/(x+2)]

= lim(x→∞) e^2

= e^2