JEE Mains · Maths · STD 12 - 5. continuity and differentiation
The number of points of discontinuity of the function \(f(\mathrm{x})=\left[\frac{\mathrm{x}^2}{2}\right]-[\sqrt{\mathrm{x}}], \mathrm{x} \in[0,4]\), where \([\cdot]\) denotes the greatest integer function is ________
- A 2
- B 4
- C 6
- D 8
Answer & Solution
Correct Answer
(D) 8
Step-by-step Solution
Detailed explanation
Check for \(\left[\frac{x^2}{2}\right]\) and \([\sqrt{x}]\) becomes integers. \(\{0,1, \sqrt{2}, 2, \sqrt{6}, \sqrt{8}, \sqrt{10}, \sqrt{12}, \sqrt{14}, 4\}\) Continuous at \(0^{+}\), continuous at \(4^{-}\) \(\left[\frac{x^2}{2}\right]=[\sqrt{x}]\), occurs at \(x=\sqrt{2}\)…
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