NIMCET 2019 Mathematics Question 2 with Solution

Question 2

Mathematics Limit of Functions Hard

Let f: R → R be defined by <span class="math-tex">\(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {x\sin \left( {\frac{1}{x}} \right)}&{if\;x > 0}\\ 0&{x \le 0} \end{array}} \right.\)</span> 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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Correct Solution: Option C

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