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Manipal MET2018MathematicsContinuity and Differentiability

If f(x)= (1+a x)- (1-b x) x for x 0 and f(0)=k and f(x) is continuous at x=0 , then k is equal to

Options

  1. Aa + b
  2. Ba - b
  3. Ca
  4. Db

Correct answer

A. a + b

Step-by-step solution

Given, f(x)= (1+a x)- (1-b x) x aligned & f(x) is continuous at x=k and f(0)=k . & _ x 0 f(x)= _ x 0 (1+a x)- (1-b x) x & ( 0 0 form ) & _ x 0 ( 1 1+a x a+ b 1-b x )=a+b & a+b=f(0)=k aligned

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