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JEE Advanced2017MathematicsContinuity and DifferentiabilityActual

Let x be the greatest integer less than or equals to x . Then, at which of the following point(s) the function f x = x cos ⁡ π x + x is discontinuous?

Options

  1. Ax = 1
  2. Bx = - 1
  3. Cx = 0
  4. Dx = 2

Correct answer

A. x = 1

Step-by-step solution

f x = x cos ⁡ π x + x π ⇒ f x = - 1 x x cos π x [ x ] is discontinuous at all integers and x cos π x is continuous everywhere. At x = 0 , f ( x ) = 0 , so it's continuous. At other integral points, f ( x ) is discontinuous.

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