JEE Main 2022 Mathematics question
Let where [t] denotes greatest integer . If m is the number of points where f is not continuous and n is the number of points where f is not differentiable, then the ordered pair (m, n) is
Answer: (3)
Solution
For x (−2, −1), f = sin(x + 2)/(x + 2); for x (−1, 1), [|x|] = 0, so f = max{2x, 0}, which is 0 on (−1, 0] and 2x on (0, 1); elsewhere f = 1. At x = −1: f(−1) = 1, the left limit is sin 1 and the right limit is 0, so f is discontinuous. At x = 1: f(1) = 1 but the left limit is 2, so
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