If f (x)= array cl 1- 4 x x^2 & if x 0 array . is continuous at x=0 Then a=

Step-by-step solution

To ensure continuity at x=0 , the left-hand limit, right-hand limit, and function value must satisfy: _ x 0^- f(x) = _ x 0^+ f(x) = f(0) From the definition, f(0) = a . The left-hand limit uses the standard form 1 - kx x^2 with k=4 , yielding: _ x 0^- 1 - 4x x^2 = 4^2 2 = 8 The right-hand limit evaluates directly: _ x 0^+ 16 + x - 4 16 + x = 0 16 = 0 Since 8 0 , no value of a produces continuity with the given definition. However, the left-hand limit calculation and available options suggest a=8 is the intended ans