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Question 1
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Let $f : \mathbb{R} \to \mathbb{R}$ be defined by $f(x)=\begin{cases} x \sin\left(\frac{1}{x}\right), & x>0,\\ 0, & x \le 0. \end{cases}$
Then
A.
f is neither continuous nor differentiable at x = 0
B.
f is continuous nor differentiable at x = 0
C.
f is continuous but not differentiable at x = 0
D.
f is not continuous but differentiable at x = 0
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