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AP EAMCET202315 May 2023Morning ShiftMathematicsContinuity and DifferentiabilityActual

If f : R R defined by f(x)= array ll x- x 2 x , & x 0 array . is continuous on R , then f(0)=

Options

  1. A1 / 2
  2. B3 / 2
  3. C1
  4. D-1

Correct answer

A. 1 / 2

Step-by-step solution

Since f(x) is also continuous on R aligned & Hence f(0)= _ h 0 f(0-h)= _ h 0 (-h)- (- h 2 ) (-h) & f(0)= _ h 0 [ h h - 1 2 ( h 2 ) ( h 2 ) ]=1- 1 2 & f(0)= 1 2 aligned

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