Question

当x趋于无穷大时,((x^2+2)/(x+2))*sin(1/x)=?

Answer 1

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