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(i)(a) Find the value L(32) of the Lagrange polynomial at x=32 and the relative error...

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Accounting

(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:
\table[[xk,,,,],[yk,,,,],[Lk(x),,,,],[ykLk(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
\table[[xk,,,,],[yk,,,,],[Lk(x),,,,],[ykLk(x),,,,]]
and by providing the required values:
L(38)
RE(f(38)~~L(38)).
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