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AP EAMCET202319 May 2023Morning ShiftMathematicsContinuity and DifferentiabilityActual

Assertion (A): If f ( x ) is not continuous at x = a , then it is not differentiable at x=a Reason (R): If f(x) is differentiable at a point, then it is continuous at that point

Options

  1. A(A) and (R) are both true, (R) is correct explanation of (A)
  2. B(A) and (R) are both true, (R) is not correct explanation of (A)
  3. C(A) is true, (R) is false
  4. D(A) is false, ( R ) is true

Correct answer

A. (A) and (R) are both true, (R) is correct explanation of (A)

Step-by-step solution

If f(x) is a differentiable function then f(x) will be also continuous at that point necessarily. Hence reason ' R ' is correct. Above concept also means that if f(x) is not continuous at any point x=a then f(x) will not be differentiable at x=a .

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