If f(x)= array cl 1- K x x x , & if x 0 1 2 , & if x=0 array . is continuous at x=0 , then the value of K is

Step-by-step solution

We have, f(x)= array cc 1- k x x x & , x 0 1 2 & , x=0 array .f(x) is continuous at x=0 aligned & _ x 0 1- k x x x = 1 2 & _ x 0 2 ² k 2 x x x = 1 2 & _ x 0 2 ( k x 2 k x 2 )² _ x 0 1 x k² 4 = 1 2 & 2 k² 4 = 1 2 aligned aligned k² &=1 k &= 1 aligned