If f:[-2,2] R is defined by f(x)= array cc 1+c x - 1-c x x & for -2 x < 0 x+3 x+1 & for 0 x 2 array . continuous on [-2,2] , then c is equal to

Step-by-step solution

Given, f:[-2,2] R f(x)= array cc 1+c x - 1-c x x , & -2 x < 0 x+3 x+1 , & 0 x 2 array . Now, LHL = _ x 0⁻ f(x) aligned & = _ h 0 1-c h - 1+c h -h & 1-c h + 1+c h 1-c h + 1+c h & = _ h 0 (1-c h)-(1+c h) -h( 1-0 + 1+0 ) & = _ h 0 -2 c h -h(1+1) =c aligned and RHL = _ x 0⁺ f(x) aligned & = _ h 0 f(0+h)= _ h 0 0+h+3 0+h+1 & = _ h 0 h+3 h+1 = 0+3 0+1 =3 aligned Since, f is continuous at x=0 . LHL = RHL c =3