Find range sin^2(xsin(1/x))

First we find the range of |xsin1x|. For |x|≤1, we clearly have the range $[0,\sin 1]$. For $x>1$, we know this function is strictly increasing, and we have limx→∞xsin1x=1 . Thus the range of |xsin1x|is [0,1], and so the range of sin2(xsin1x) is [0,sin21]