The values of a and b , so that the function f(x)= array l x+ a 2 x, 0 x 4 2 x x+ b , 4 x 2 acos 2 x- b x, 2 < x array . is continuous for 0 x , are respectively given by

Step-by-step solution

As the given function is continuous at x= 4 and 2 , we get array ll & _ x ⁻ 4 f (x)= _ x ⁺ 4 f (x) & _ x 4 (x+ a 2 x)= _ x 4 (2 x x+ b ) & 4 + a = 2 4 + b & a - b = 4 & Also, _ x ⁻ 2 f (x)= _ x ⁺ 2 f (x) & _ x 2 2 x x+ b = _ x 2 a 2 x- b x & 0+ b =- a - b . & a +2 ~b =0 array Solving equations (i) and (ii), we get a= 6 and b= - 12