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AP EAMCET2009MathematicsContinuity and Differentiability

If f: R R is defined by f(x)= array cc 2 x- 2 x 2 x x , & if x 0 a, & if x=0 array . , then the value of a so that f is continuous at 0 is

Options

  1. A2
  2. B1
  3. C-1
  4. D0

Correct answer

D. 0

Step-by-step solution

Given, f(x)= array cc 2 x- 2 x 2 x x , & if x 0 a, & if x=0 array . Now, _ x 0 f(x)= _ x 0 2 x- 2 x 2 x x aligned & ( 0 0 form ) & = _ x 0 2 x-2 2 x 2( x-x x) & = _ x 0 2-2 2(1-0) =0 aligned Since, f(x) is continuous at x=0 f(0)= _ x 0 f(x) a=0

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