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COMEDK202510 May 2025Evening ShiftMathematicsContinuity and DifferentiabilityActual

The function f(x)= array c |x| x , if x 0 0, if x=0 array . is discontinuous at

Options

  1. Ax=0
  2. Bx <0
  3. Cx>1
  4. Dx>0

Correct answer

A. x=0

Step-by-step solution

The function is defined as f(x) = |x| x for x 0 and f(0) = 0 . For x > 0 , |x| = x , so f(x) = x x = 1 . For x Evaluating the limits at x = 0 : Left hand limit: _ x 0⁻ f(x) = _ x 0⁻ (-1) = -1 . Right hand limit: _ x 0⁺ f(x) = _ x 0⁺ (1) = 1 . Since the left hand limit and right hand limit are not equal, the limit _ x 0 f(x) does not exist. Therefore, the function is discontinuous at x = 0 . Answer: x=0

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