JEE Mains · Maths · STD 12 - 5. continuity and differentiation
Let \(f:[-1,2] \rightarrow \mathrm{R}\) be given by \(f(x)=2 x^2+x+\left[x^2\right]-[x]\), where \([t]\) denotes the greatest integer less than or equal to \(t\). The number of points, where \(f\) is not continuous, is :
- A \(6\)
- B \(3\)
- C \(4\)
- D \(5\)
Answer & Solution
Correct Answer
(C) \(4\)
Step-by-step Solution
Detailed explanation
Doubtful points : \(-1,0,1, \sqrt{2}, \sqrt{3}, 2\) at \(\mathrm{x}=\sqrt{2}, \sqrt{3}\) \(f(x)=\left(2 x^2+x-[x]\right)+\left[x^2\right]=\text { Discount }\) \(\underset{\text { Cont. }}{\downarrow} \quad \underset{\text { Cont. }}{\downarrow}\) at \(\mathrm{x}=-1\):…
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