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COMEDK2018MathematicsContinuity and Differentiability

The function f(x)= ( _ e (1+a x)- _ e (1-b x) x ) is undefined at x=0 . The value which should be assigned to f at x=0 so that it is continuous at x=0 is

Options

  1. Aa+b 2
  2. Ba+b
  3. C_ e (a b)
  4. Da-b

Correct answer

B. a+b

Step-by-step solution

We have, f(x)= _ e (1+a x)- _ e (1-b x) x = _ x 0 _ e (1+a x)- _ e (1-b x) x [ 0 0 . form ] Applying L'Hospital rule, _ x 0 a 1+a x + b 1-b x 1 = a 1 + b 1 1 =a+b

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