JEE Mains · Maths · STD 12 - 5. continuity and differentiation
Let \(f\left( x \right) = x\left| x \right|\,,\,g\left( x \right) = \sin \,x\) and \(h\left( x \right) = \left( {gof} \right)\left( x \right)\). Then
- A \(h(x)\) is not differentiable at \(x\, = 0\).
- B \(h(x)\) is differentiable at \(x\, = 0\), but \(h'(x)\) is not continuous at \(x\, = 0\)
- C \(h'(x)\) is continuous at \(x\, = 0\) but it is not differentiable at \(x\, = 0\)
- D \(h'(x)\) is differentiable at \(x\, = 0\)
Answer & Solution
Correct Answer
(C) \(h'(x)\) is continuous at \(x\, = 0\) but it is not differentiable at \(x\, = 0\)
Step-by-step Solution
Detailed explanation
Let \(f\left( x \right) = x\left| x \right| = x\left| x \right|,g\left( x \right) = \sin x\) and \(h\left( x \right) = gof\left( x \right) = g\left[ {f\left( x \right)} \right]\)…
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