$($i$)($a$)$ Find the value $L(32)$ of the Lagrange polynomial at $x=32$ and the relative error in the approximation of $f(32)$ by $L(32).$

$($b$)$ Show your work by filling in the standard table for the method showing the process of evaluation of the Lagrange polynomial at the given point:

$\backslash$table$[[x_k,,,,],[y_k,,,,],[L_k(x),,,,],[y_k{L}_k(x),,,,]]$

$($c$)$ Accordingly,

$L(32)=$

and the relative error in question is given by

$RE(f(32)$~~$L(32))$

$$

$($ii$)$ Find the value $L(38)$ of the Lagrange polynomial at $x=38$ and the relative error in the approximation of $f(38)$ by $L(38).$

Proceed then as in the previous part by filling in the standard table

$\backslash$table$[[x_k,,,,],[y_k,,,,],[L_k(x),,,,],[y_k{L}_k(x),,,,]]$

and by providing the required values:

$L(38)$

$RE(f(38)$~~$L(38)).$