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Mathematics - Continuity - Differentiability Question with Solution | TestHub

MathematicsContinuity - DifferentiabilityDifferentiabilityMedium2 minQB

MathematicsMediummultiple choice

Define $f (0) = 0$ and $f (x) = x^{m} cos (x - 1/ x)$ for $x > 0$ . Which statements are true?

Options:(select one or more)

Answer:

A, C, D

Solution:

Continuity holds exactly when $m > 0$ , because the oscillatory factor is bounded. The difference quotient is $x^{m - 1} cos (x - 1/ x)$ , which tends to 0 when $m > 1$ and fails to converge for $0 < m \leq 1$ .

Stream:JEESubject:MathematicsTopic:Continuity - DifferentiabilitySubtopic:Differentiability

⏱ 2mℹ️ Source: QB

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