MHT CET2012MathematicsContinuity and Differentiability

If f(x)= array cl (1+2 a x)- (1-b x) x , & x 0 k & , x=0 array . continuous at x=0 , then value of k is

Options

Ab+a
Bb-2 a
C2 a-b
D2 a+b

Correct answer

D. 2 a+b

Step-by-step solution

Given, f(x)= array cl (1+2 a x)- (1-b x) x , & x 0 k & , x=0 array . is continuous at x=0 . f(0)= _ x 0 (1+2 a x)- (1-b x) x ( 0 0 . form ) k= _ x 0 1 2 a x+1 (2 a)- 1 1-b x (-b) +1 (by 'L' Hospital's rule) k= 2 a 0+1 + b 1-0 =2 a+b

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