Chapter 3.4, Problem 6E

The following table lists data for the function described by $f(x)=e^{0.1x^2}$.

Approximate $f(1.25)$ by using $H_5(1.25)$ and $H_3(1.25),$ where $H_5$ uses the nodes $x_0=1,x_1=2,$ and $x_2=3$ and $H_3$ uses the nodes ${\bar{x}}_0=1$ and ${\bar{x}}_1=\mathrm{1.5.}$ Find error bounds for these approximations.