Question

求极限lim（x-->无穷）（（2x^3+x）sin2/x）/(x^2+1)

Answer 1

设t = 1/x

原式 = (2/t^3 + 1/t ) sin2t / (1/t^2 + 1)

=(2 + t^2) sin2t / (t^3+t)

=2(2+t^2)t / (t^3+t)

=2(2+t^2) / (1 + t^2)

=2*2

=4