JEE Mains · Maths · STD 11 - 12. limits
Let \([t]\) denote the greatest integer \(\leq t\) and \(\mathop {\lim }\limits_{x \to 0} x\left[\frac{4}{x}\right]=A .\) Then the function. \(\mathrm{f}(\mathrm{x})=\left[\mathrm{x}^{2}\right] \sin (\pi \mathrm{x})\) is discontinuous, when \(\mathrm{x}\) is equal to
- A \(\sqrt{A+5}\)
- B \(\sqrt{A+1}\)
- C \(\sqrt{A}\)
- D \(\sqrt{A+21}\)
Answer & Solution
Correct Answer
(B) \(\sqrt{A+1}\)
Step-by-step Solution
Detailed explanation
\(A=\lim _{x \rightarrow 0} x\left[\frac{4}{x}\right]=\lim _{x \rightarrow 0} x\left(\frac{4}{x}\right)-x\left\{\frac{4}{x}\right\}=4\) \(f(\mathrm{x})=\left[\mathrm{x}^{2}\right] \sin (\pi \mathrm{x})\) will be discontinuous at nonintegers…
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