IGNOU MTE 10 2018 - Using finite differences, show that the data x

Question

Using finite differences, show that the data

x	− 3	− 2	− 1	0	1	2	3
f ( x)	13	7	3	1	1	3	7

represents a second degree polynomial. Obtain this polynomial using interpolation
and find f (2.5) .

14 Feb 2018

Answer :

Word Count : 321

We are asked to show that the given data represents a second-degree polynomial using finite differences and then find the polynomial and $f(2.5)$. The data is: | $x$ | -3 | -2 | -1 | 0 | 1 | 2 | 3 | | ------ | -- | -- | -- | - | - | - | - | | $f(x)$ | 13 | 7 | 3 | 1 |

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x	1	2	3	4	5
$\sqrt\frac{{1+x^4}}{x^4}$	1.414	1.031	1.007	1.002	1.001