Answer
$(a)$ $\lim_{x\to0}f(x)=0$
$(b)$ $\lim_{x\to\pi/3}f(x)=\dfrac{\pi}{6}$
Work Step by Step
$f(x)=x\cos x$
The graph of the function is shown below:
$(a)$ $\lim_{x\to0}f(x)$
From the graph, it can be seen that when $x$ approaches $0$ from the left and from the right, $f(x)$ approaches $0$
$\lim_{x\to0}f(x)=0$
$(b)$ $\lim_{x\to\pi/3}f(x)$
From the graph, it can be seen that when $x$ approaches $\dfrac{\pi}{3}$ from the left and from the right, $f(x)$ approaches $\dfrac{\pi}{6}$
$\lim_{x\to\pi/3}f(x)=\dfrac{\pi}{6}$
