Question

求极限lim(x→+∞)[（x+3）/（x+2）]^x,要具体过程,

Answer 1

lim(x->∞) [(x+3)/(x+2)]^x

= lim(x->∞) [((x+2)+1)/(x+2)]^x

= lim(x->∞) [1 + 1/(x+2)]^x

= lim(x->∞) [1 + 1/(x+2)]^[(x+2) * x/(x+2)]

= e^lim(x->∞) x/(x+2)

= e^lim(x->∞) 1/(1+2/x)

= e^[1/(1+0)]

= e