Answer
a. No.
b. Yes. $0$
c. No.
Work Step by Step
Use the figure in the Exercise, given the piecewise function: $f(x)=\begin{cases} 0\hspace1.7cm x\leq0 \\ sin\frac{1}{x}\hspace1cm x\gt0 \end{cases}$
a. No. The limit $\lim_{x\to0^+}f(x)$ does not exist because $ sin\frac{1}{x}$ oscillates in a range $[-1,1]$ when $x\to0^+$
b. Yes. The limit $\lim_{x\to0^-}f(x)=0$ exist.
c. No. The limit $\lim_{x\to0}f(x)$ does not exist because $\lim_{x\to0^+}f(x)$ does not exist.
