JEE Main20248 Apr 2024Evening ShiftMathematicsContinuity and DifferentiabilityActual

For a , b >0 , let f(x)= array cc (( a +1) x)+ b x x , & x 0 array . be a continous function at x=0 . Then b a is equal to :

Options

Correct answer

A. 6

Step-by-step solution

aligned & _ x 0 f(x)=f(0)=3 & _ x 0⁺ a x+b^2 x^2 - a x b a x x =3 & _ x 0⁺ a x+b^2 x^2-a x b a x^ 3 / 2 ( a x+b^2 x^2 + a x ) & _ x 0⁺ b^2 b a ( a+b^2 x + a ) & b a 2 a b 2 a =3 b a =6 aligned

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