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JEE Main 2012 Mathematics question

MathematicsContinuity and DifferentiabilityJEE Main 2012

Let f : [1, 3] → R be a function satisfying , for all x ≠ 2 and f(2) = 1, where R is the set of all real numbers and [x] denotes the largest integer less than or equal to x. Statement 1: exists. Statement 2: f is continuous at x = 2.

Answer: (4)

Solution

As , [x] = 1, so and both bounds tend to 2: the left limit exists

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Question ID VK-103614