Limit of $x^5\cos\left(\frac1x\right)$ as $x$ approaches $0$ Find the limit of $x^5\cos\left(\frac1x\right)$ as $x$ approaches $0$.
Can I just substitute $0$ to $x^5$? But what would be $\cos\left(\frac10\right)$ be?
I could solve for $-x^4\le x^4\cos(1/x)\leq x^4$
in which limit of $x^4$ is and $-x^4=0$ and by sandwich theorem limit=0
but is there a method to solve it without doing so

Notice, $-1\le \cos \left(\frac 1x\right)\le 1\ \ \forall  \ \ x\in \mathbb{R}$, hence 
$$\lim_{x\to 0}x^5\cos\left(\frac 1x\right)=0$$
