I'm trying to figure out how to calculate the limit of

$f(x)= \begin{cases}
 \frac{3}{2}\cdot x^{\frac{1}{2}}\cdot\sin\left(\frac{1}{x}\right)-\frac{1}{\sqrt{x}}\cdot\cos\left(\frac{1}{x}\right) & x > 0 \\
 \\
 0 & x≤0 \\ \end{cases}$

as $x$ tends to $0^{+}$ I know it doesn't exist and tends to $-∞$, I've been trying forever to prove there exist two functions that are bigger/smaller than $f$ in order to use the squeeze rule but I'm begging to think there is some other easier way..