f(x)= cases ^3( 3 ) (1+3 x) ( ⁻¹ x )^2 (e^ 5 x -1 ) x , & x 0 a, & x=0 cases is continuous in [0,1] , if ' a ' equals to

Step-by-step solution

We have, f(x)= array cc ^3( x ) (1+3 x) x ( ⁻¹ x )^2 (e^ 5 x -1 ) , & x 0 a, & x=0 array . For continuity in [0,1], f(0)=f (0⁺ ) , otherwise it is discontinuous. aligned & _ x 0⁺ ^3( x ) (1+3 x) x ( ⁻¹ x )^2 (e^ 5 x -1 ) & = _ x 0⁺ [ 3 5 ^3 x ( x )^3 ( x )^2 ( ⁻¹ x )^2 . & .x (1+3 x) 3 x 5 x e^ 5 x -1 ] & = 3 5 _ x 0⁺ ^3 x ( x )^3 ( x )^2 ⁻¹ x (1+3 x) 3 x & 5 x e^ 5 x -1 =a aligned a= 3 5