(3+x)/(6+x)的(x-1)/2次方,当x趋近于无穷大时,求它的极限

题目

(3+x)/(6+x)的(x-1)/2次方,当x趋近于无穷大时,求它的极限

答案

lim(x→∞)[(3+x)/(6+x)]^[(x-1)/2]= {lim(x→∞)1/[1+3/(x+3)]^[(x+3)/3]}^(3/2)*lim(x→∞)1/[1+3/(x+3)]^(-2) =1/e^(3/2)=e(-3/2)