The values of a and b for which the function f(x)= array cc 1+| x|^ a/| x| , & - 6 x 0 b, & x=0 e^ 2 x / 3 x , & 0 x 6 array . is continuous at x=0 are

Step-by-step solution

f(x) array cc (1+| x|)^ a | x| & , - 6 x 0 b & x=0 e^ 2 x 3 x & , 0 x 6 array . For f(x) to be continuous at x=0 aligned & _ x 0⁻ f(x)=f(0)= _ x 0⁻ f(x) ... (i) & _ x 0⁻ (1+| x|)^ a | x| & =e^ _ x 0 (| x| a | x| ) =e^a (1^ form) aligned Now, _ x 0⁺ e^ 2 x 3 x = _ x 0 e^ ( 2 x 2 x 2 x ) ( 3 x 3 x 3 x ) =e^ 2 3 From (i) e^a=b=e^ 2 3 a= 2 3 , b=e^ 2 3