JEE Main20252 Apr 2025Evening ShiftMathematicsLimitsActual

If _ x 0 (2 x)+a (4 x)-b x^4 is finite, then (a+b) is equal to :

Options

A1 2
B0
C3 4
D-1

Correct answer

A. 1 2

Step-by-step solution

_ x 0 2 x+a 4 x-b x^4 = finite aligned & L= 1- (2 x)^2 2 + (2 x)^4 4 +a 1- (4 x)^2 2 + (4 x)^4 4 -b . x^4 & L= (1+a-b)-x^2(2+8 a)+x^4 ( 2 3 + 32 3 a )+x^6() x^4 aligned aligned & 1+ a - b =0 and 2+8 a =0 a =- 1 4 & ~b = a +1 & =- 1 4 +1= 3 4 & a + b =- 1 4 + 3 4 = 1 2 aligned

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