Q$\mathrm{.}3.$ Develop a second order $f_2(x)$ interpolating polynomial using newton interpolation method for given function below:

$f(x)=e^x+2$

For the data points $x_0=0,x_1=1$ and $x_2=2.$ Then, calculate true and approximate values at $x=1\mathrm{.}5$ and find true error.

I