JEE Main20245 Apr 2024Morning ShiftMathematicsContinuity and DifferentiabilityActual

If the function f(x)= 3 x+ x- 3 x x^3 , x R , is continuous at x=0 , then f(0) is equal to :

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Correct answer

D. -4

Step-by-step solution

f(x)= 3 x+ x- 3 x x^3 is continuous at x =0 _ x 0 = 3 x- (3 x)^3 |3 + + (x- x^3 |3 )- (1- (3 x)^2 2 ) x^3 =f(0) aligned & _ x 0 = - +x(3+ )+ 9 x^2 |2 + ( -27 |3 - |3 ) x^3 x^3 =f(0) & for exist & =0,3+ =0,- 27 |3 - |3 =f(0) aligned aligned & =-3,- 27 6 - (-3) 6 =f(0) & f(0)= -27+3 6 =-4 aligned

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