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Manipal MET2012MathematicsContinuity and Differentiability

The function f(x)= (1+a x)- (1-b x) x is not defined 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. Ba+b
  3. Ca+ b
  4. DNone of these

Correct answer

B. a+b

Step-by-step solution

For f(x) to be continuous, we must have aligned & f(0)= _ x 0 f(x) & _ x 0 (1+a x)- (1-b x) x = & _ x 0 a (1+a x) a x + b (1-b x) -b x = & a 1+b 1 [ using, _ x 0 (1+x) x =1 ] = & a+b & f(0)=a+b aligned

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