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AP EAMCET2003MathematicsContinuity and Differentiability

If f(x) array cl 1+k x - 1-k x x , & for -1 x < 0 2 x^2+3 x-2, & for 0 x 1 array . is continuous at x=0 , then k is equal to

Options

  1. A-1
  2. B-2
  3. C-3
  4. D-4

Correct answer

B. -2

Step-by-step solution

Since, f(x) is continuous at x=0 _ h 0 f(0-h)= _ h 0 f(0+h) _ h 0 1-k h - 1+k h -h = _ h 0 2 h^2+3 h-2 _ h 0 1 2 (1-k h)^ - k 2 + 1 2 (1+k)^ - k 2 -1 =-2 k 2 + k 2 =-2 k=-2

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