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JEE Main2012MathematicsContinuity and DifferentiabilityActual

Statement 1: A function f: R R is continuous at x₀ if and only if _ x x₀ f(x) exists and _ x x₀ f(x)=f (x₀ ) Statement 2: A function f: R R is discontinuous at x₀ if and only if, _ x x₀ f(x) exists and _ x x₀ f(x) f (x₀. )

Options

  1. AStatement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.
  2. BStatement 1 is false, Statement 2 is true.
  3. CStatement 1 is true, Statement 2 is true, Statement 2 is a correct explanation of Statement 1.
  4. DStatement 1 is true, Statement 2 is false.

Correct answer

D. Statement 1 is true, Statement 2 is false.

Step-by-step solution

Statement-1 is true. It is the definition of continuity. Statement -2 is false.

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