Let t denote the greatest integer ≤ t and lim x → 0 ⁡ x 4 x = A . Then the function, f x = x 2 sin ⁡ π x is discontinuous, when x is equal to:

log x → 0 ⁡ 4 x - 4 x = A ⇒ log x → O ⁡ 4 - x 4 x = A ⇒ 4 - 0 ⇒ A = 4 Hence, for 5 , f x is discontinuous as it is an non-integral value.

Mathematics - Continuity - Differentiability Question with Solution | TestHub

MathematicsContinuity - DifferentiabilityContinuity- MiscellaneousEasy2 minPYQ_2020

MathematicsEasysingle choice

Let $[t]$ denote the greatest integer $\leq t$ and $\lim_{x \to 0} x [\frac{4}{x}] = A .$ Then the function, $f (x) = [x^{2}] \sin (π x)$ is discontinuous, when $x$ is equal to:

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Answer:

Solution:

$\log_{x \to 0} (\frac{4}{x} - \{\frac{4}{x}\}) = A \Rightarrow \log_{x \to O} 4 - x \{\frac{4}{x}\} = A$

$\Rightarrow 4 - 0$

$\Rightarrow A = 4$

Hence, for $\sqrt{5}$ , $f (x)$ is discontinuous as it is an non-integral value.

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

⏱ 2mℹ️ Source: PYQ_2020

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