Consider, f(x)= array ll e^ (x-2) 5^x + 1 3 x ₂ ( (4^x )^3 ) -e^2 (x-2) x , & x 0 (( 5 )^x-1 ) (e^ x^2+2 -e^2 ) (2 x- 2 x) , & x 0 array . . If _ x 0 f(x) exists then is equal to

Step-by-step solution

aligned & _ x 0⁺ e^2 (5^ ( x(x-2) 2 ) -1 ) 2 x(x-2) 2 x x = 1 2 e^2 5 & _ x 0⁻ (e^2 (( 5 )^x-1 ) ) (e^ x^2 -1 ) x 2 x x ( 1- x x^2 ) x^2 = e^2 5 = e^2 2 5 & =1 aligned