# prove that a function is not bounded

Prove that $$2x\sin{1\over x^2}-{2\over x}\cos{1\over x^2}$$ is not bounded when $x\to 0$ I tried to find two sequences that converges to $\infty$ and $-\infty$ but I can´t; I also derived the function but its derivative is much more complicated than the function so I can´t find the points where there are maximum and minimum of the function so I would really appreciate your help

Try $x_n = (2n\pi)^{-1/2}$ for $n = 1, 2,...$ and see what happens....