Let f ( x ) = cos (⌊ π / x ⌋) cos ( 2 π ( x − 1 ) ) . At which listed points is f continuous?

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Mathematics - Continuity - Differentiability Question with Solution | TestHub

MathematicsContinuity - DifferentiabilityContinuity- MiscellaneousMedium2 minQB

MathematicsMediummultiple choice

Let $f (x) = cos (⌊ π / x ⌋) cos (\frac{π}{2} (x - 1))$ . At which listed points is $f$ continuous?

Options:(select one or more)

Answer:

B, C

Solution:

The function is undefined at 0. The integer $⌊ π / x ⌋$ is locally constant near both $x = 1$ and $x = 2$ (equal to 3 and 1 respectively), so the product is continuous at both points.

Stream:JEESubject:MathematicsTopic:Continuity - DifferentiabilitySubtopic:Continuity- Miscellaneous

⏱ 2mℹ️ Source: QB

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