The value of `Deltalogf(x)+Delta^(2)(3^(x))` is

Options

A. `log[1+(Deltaf(x))/(f(x))]+4.3^(x)`
B. `log[1+(Deltaf(x))/(f(x))]+3^(x)`
C. `log[(Deltaf(x))/(1+f(x))]+4.3^(x)`
D. `log[(Deltaf(x))/(1+f(x))]+3^(x)`

Answer

A

Explanation

`Delta log f(x)+Delta^(2)(3^(x))`
`log f(x+h)-log f(x)+(E-)^(2)3^(x)`
`= log [ (f(x+h))/(f(x))]+(E^(2)-2E+1)3^(x)`
`= log [ (E(x+h))/(f(x))]+E^(2)(3^(x))-2E(3^(x))+3^(x)`
`= log [ (E(x+h))/(f(x))]+E^(2)(3^(x))-2E(3^(x))+3^(x)`
`=log[1+(Delta f(x))/(f(x))]+3^(x)(9-6+1)`
`=log[1+(Delta f(x))/(f(x))]+4*e^(x)`