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AP EAMCET2006MathematicsContinuity and Differentiability

If f(x)= cases 1- 2 x -4 x & if x 4 a & if x= 4 cases is continuous at 4 , then a is equal to

Options

  1. A4
  2. B2
  3. C1
  4. D1 / 4

Correct answer

D. 1 / 4

Step-by-step solution

f(x)= cases 1- 2 x -4 x , & if x 4 a, & if x= 4 cases _ x 4 f(x)= _ x 4 1- 2 x -4 x = _ x 4 - 2 x -4 (By L' Hospital's rule) = 2 1 2 4 = 1 4 Since f(x) is continuous at x= 4 . _ x 4 f(x)=f ( 4 ) 1 4 =a

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