Question

4(a) Using the following data, $f(0) = 1, f(1) = 3, f(3) = 55$ find the unique polynomial of degree 2 or less which fits the given data. Also, obtain a bound on the error. (b) If $f(x) = \frac{1}{x^2}$, find the divided difference of $f[x_1, x_2, x_3, x_4]$ (c) Obtain the piecewise linear interpolating polynomial for the function $f(x)$ defined by data $\begin{array}{|c|c|c|c|c|} \hline x & 1.0 & 2.0 & 4.0 & 8.0 \\ \hline f(x) & 3 & 7 & 21 & 73 \\ \hline \end{array}$ and estimate the values of $f(3)$ and $f(7)$.

          4(a) Using the following data,
$f(0) = 1, f(1) = 3, f(3) = 55$
find the unique polynomial of degree 2 or less which fits the given data.
Also, obtain a bound on the error.
(b) If $f(x) = \frac{1}{x^2}$, find the divided difference of $f[x_1, x_2, x_3, x_4]$
(c) Obtain the piecewise linear interpolating polynomial for the function $f(x)$ defined by
data
$\begin{array}{|c|c|c|c|c|}
\hline
x & 1.0 & 2.0 & 4.0 & 8.0 \\
\hline
f(x) & 3 & 7 & 21 & 73 \\
\hline
\end{array}$
and estimate the values of $f(3)$ and $f(7)$.

4(a) Using the following data,
f(0) = 1, f(1) = 3, f(3) = 55
find the unique polynomial of degree 2 or less which fits the given data.
Also, obtain a bound on the error.
(b) If f(x) = (1)/(x^2), find the divided difference of f[x1, x2, x3, x4]
(c) Obtain the piecewise linear interpolating polynomial for the function f(x) defined by
data
x 1.0 2.0 4.0 8.0

f(x) 3 7 21 73
and estimate the values of f(3) and f(7).

Added by Laura P.

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