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AP EAMCET202422 May 2024Morning ShiftMathematicsContinuity and DifferentiabilityActual

Let f(x)= array cc 0, & x=0 2-x, & for 0 x 1 2, & for x=1 1 2 -x, & for 1 x 2 -3 2 , & for x 2 array . then which of the following is true

Options

  1. Af is right continuous at x=0
  2. Bf is left continuous at x=1
  3. Cf is right continuous at x=1
  4. Df is continuous at x=2

Correct answer

D. f is continuous at x=2

Step-by-step solution

For x=0 aligned & _ x 0⁻ f(x)= does not exist as f is not defined for x 0 & _ x 0⁺ f(x)=2, f(0)=0 aligned f is not continuous for x=0 For x=1 ; _ x 1⁻ f(x)=1, _ x 1⁺ f(x)= -1 2 , f(1)=2 So, f is not continuous for x=1 For x=2 ; _ x 2⁻ f(x)= -3 2 , _ x 2⁺ f(x)= -3 2 , f(2)= -3 2 So, f is continuous at x=2 .

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