Chapter 3.5, Problem 21ES

(a)

To determine

The average weight curve for each sample by use of natural cubic spline.

(b)

To determine

An approximation for ${\displaystyle \underset{0}{\overset{0.1}{\int }}{e}^{2x}dx}$ by evaluating ${\displaystyle \underset{0}{\overset{0.1}{\int }}s\left(x\right)dx}$.

(c)

To determine

To estimate: The value of ${\max }_{0\le x\le 0.1}\left|f\left(x\right)-s\left(x\right)\right|$, and $\left|{\displaystyle \underset{0}{\overset{0.1}{\int }}f\left(x\right)dx}-{\displaystyle \underset{0}{\overset{0.1}{\int }}s\left(x\right)dx}\right|$.

(d)

To determine

The cubic spline S with natural boundary conditions.