JEE Mains · Maths · STD 12 - 5. continuity and differentiation
Let \([t]\) denote the greatest integer \(\leq t\). The number of points where the function \(f(x)=[x]\left|x^{2}-1\right|+\sin \left(\frac{\pi}{[x]+3}\right)-[x+1], x \in(-2,2)\) is not continuous is ..... .
- A \(2\)
- B \(4\)
- C \(6\)
- D \(8\)
Answer & Solution
Correct Answer
(A) \(2\)
Step-by-step Solution
Detailed explanation
\(f(x)=[x]\left|x^{2}-1\right|+\sin \frac{\pi}{[x+3]}-[x+1]\) \(f(x)=\{3-2 x^{2}, \quad\quad\quad-2\) \(\quad\quad\quad x^{2}, \quad\quad\,\,\quad\quad\quad -1 \leq x<0\) \(\quad\quad\quad \frac{\sqrt{3}}{2}+1 \quad\quad\quad\quad 0 \leq x<1\)…
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