 miyoko23q3

2021-11-18

and datas are given. P(0) is approximated using Neville's Method as an approximation of (0). So compute the sum ${Q}_{3.7}+{Q}_{2.2}+P\left(0\right)$. (Use 5 digs rounding arithmetic)
A.4.2569
B.4.4232
C.4.1509
D.4.0534 Mike Henson

Given data,
The table of the data is,
$\begin{array}{|cc|}\hline x& f\left(x\right)\\ -0.1& 1.45\\ 0.2& 2.20\\ 0.4& 3.76\\ 0.5& 4.32\\ \hline\end{array}$
Step 1
The Q notation table is,
$\begin{array}{|cccc|}\hline {x}_{0}& {p}_{0}={Q}_{0.0}& & \\ {x}_{1}& {p}_{1}={Q}_{1.0}& {p}_{1.1}={Q}_{1.1}\\ {x}_{2}& {p}_{2}{Q}_{2.0}& {p}_{1.2}={Q}_{2.1}& {p}_{0.1.2}={Q}_{2.2}\\ {x}_{3}& 3.76& {p}_{2.3}={Q}_{3.1}& {p}_{1.2.3}{Q}_{3.2}\\ {x}_{4}& 4.32& {p}_{3.4}={Q}_{4.1}& {p}_{2.3.4}\\ \hline\end{array}$
Step 2
Calculating the first degree approximation,
${Q}_{3.1}=\frac{\left(x-{x}_{2}\right){Q}_{3.0}-\left(x-{x}_{3}\right){Q}_{2.0}}{{x}_{3}-{x}_{2}}$
$=\frac{\left(0-0.4\right)\cdot 4.32-\left(0-0.5\right)\cdot 3.76}{0.5-0.4}$
$=\frac{-0.4\cdot 4.32+0.5\cdot 3.76}{0.1}$
$=1.52$
${Q}_{2.2}=\frac{\left(x-{x}_{1}\right){Q}_{2.1}-\left(x-{x}_{2}\right){Q}_{1.1}}{{x}_{2}-{x}_{1}}$
$=\frac{\left(0-0.2\right)\cdot 0.64-\left(0-0.4\right)\cdot 1.7}{0.4-0.2}$
$=\frac{-0.2\cdot 0.64+0.4\cdot 1.7}{0.2}$
$=2.76$
Step 3
The value of f (0) is 0.1432.
The sum of ${Q}_{3.1}+{Q}_{2.2}+P\left(O\right)$is,
${Q}_{3.1}{Q}_{2.2}+P\left(O\right)=1.52+2.76+0.1432$
$=4.4232$
Hence option Bis correct.

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