Define f ( 0 ) = 0 and f ( x ) = ( sin − 1 x ) 2 cos ( 1/ x ) for x  = 0 , − 1 ≤ x ≤ 1 . Which statements are true?

Both factors are continuous and differentiable for interior nonzero x (with the usual one-sided interpretation at endpoints). At 0 , ∣ f ( x ) ∣ ≤ C x 2 , so it is also continuous and differentiable there, but the listed true claims are (B) and (D).

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Mathematics - Continuity - Differentiability Question with Solution | TestHub

MathematicsContinuity - DifferentiabilityDifferentiabilityMedium2 minQB

MathematicsMediummultiple choice

Define $f (0) = 0$ and $f (x) = (sin^{- 1} x)^{2} cos (1/ x)$ for $x \neq = 0, - 1 \leq x \leq 1$ . Which statements are true?

Options:(select one or more)

Answer:

B, D

Solution:

Both factors are continuous and differentiable for interior nonzero $x$ (with the usual one-sided interpretation at endpoints). At $0, ∣ f (x) ∣ \leq C x^{2}$ , so it is also continuous and differentiable there, but the listed true claims are (B) and (D).

Stream:JEESubject:MathematicsTopic:Continuity - DifferentiabilitySubtopic:Differentiability

⏱ 2mℹ️ Source: QB

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