Let f: R → R be defined by \(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {x\sin \left( {\frac{1}{x}} \right)}&{if\;x > 0}\\ 0&{x \le 0} \end{array}} \right.\) Then

f is not continuous but differentiable at x = 0

f is neither continuous nor differentiable at x = 0

f is continuous nor differentiable at x = 0

f is continuous but not differentiable at x = 0

Let f: R → R be defined by \(f\left( x \right) = \left\{ {\begin{a

1.	Let f: R → R be defined by \(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {x\sin \left( {\frac{1}{x}} \right)}&{if\;x > 0}\\ 0&{x \le 0} \end{array}} \right.\) 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
Answer» D. f is not continuous but differentiable at x = 0

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Let f: R → R be defined by \(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {x\sin \left( {\frac{1}{x}} \right)}&{if\;x > 0}\\ 0&{x \le 0} \end{array}} \right.\) Then

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