Answer
See explanations.
Work Step by Step
Step 1. Using the figure provided by the Exercise, the function is sandwiched between two lines $y=\pm x$ or $-x\leq xsin\frac{1}{x}\leq x$. This is because the function $sin\frac{1}{x}$ oscillates within $[-1,1]$
Step 2. Find the limits of the two end functions: $\lim_{x\to0}(-x)=0$ and $\lim_{x\to0}(x)=0$
Step 3. Based on the Sandwich Theorem, we conclude that $\lim_{x\to0}(xsin\frac{1}{x})=0$
