当x趋于无穷大时,((x^2+2)/(x+2))*sin(1/x)=?
问题描述：
当x趋于无穷大时,((x^2+2)/(x+2))*sin(1/x)=?
答
lim(x→∞) ((x^2+2)/(x+2))*sin(1/x)
=lim(x→∞) ((x^2+2)/(x+2))*(1/x)
=lim(x→∞) ((x^2+2)/(x^2+2x))
=lim(x→∞) ((1+2/x^2)/(1+2/x))
=lim(x→∞) (1)/(1)
=1