JEE Mains · Maths · STD 11 - 12. limits
For each \(x\,\in R,\) let \([x]\) be the greatest integer less than or equal to \(x.\) Then \(\mathop {\lim }\limits_{x \to {0^ + }} \frac{{x([x] + [x])\,\sin \,[x]}}{{\left| x \right|}}\) is equal to
- A \(-\,sin\,1\)
- B \(0\)
- C \(1\)
- D \(sin\,1\)
Answer & Solution
Correct Answer
(A) \(-\,sin\,1\)
Step-by-step Solution
Detailed explanation
\(\mathop {\lim }\limits_{x \to {0^ + }} \frac{{x\left( {\left[ x \right] + \left| x \right|} \right)\sin \left[ x \right]}}{{\left| x \right|}}\) \(x \to {0^ - }\)…
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