Let $r(t) = (\cos (4t), \sin (4t), t^2).$ We have to find the velocity of the particle at time $t$ and describe what happens when $t \to \infty$.
Since $r(t) = (\cos (4t), \sin (4t), t^2)$, $$v(t) = r'(t) = (-4\sin(4t),4\cos(4t),2t)$$
Thus as $t \to \infty$, the $z$ component of velocity tends to $\infty$. Is the explanation correct?