IGNOU BMTE 144 2026 - For the following data, use Gauss backward difference method to obtain

Question

For the following data, use Gauss backward difference method to obtain the interpolating polynomial f(x):

x	0.1	0.2	0.3	0.4	0.5
f(x)	1.40	1.56	1.76	2.00	2.28

Hence, find the value of f(0.45).

09 Jan 2026

Answer :

Word Count : 426

First, tabulate the backward differences for the given data. Denote (x_0 = 0.1, x_1 = 0.2, \dots, x_4 = 0.5) and (h = 0.1). | x | f(x) | Δf | Δ²f | Δ³f | Δ⁴f | | --- | ---- | ---- | ---- | ---- | ---- | | 0.1 | 1.40 | | | | | | 0.2 | 1.56 | 0.16 | | | | | 0.3 | 1.76 | 0.20 | 0.04 | | | | 0.4 | 2.00 | 0.24 | 0.04 | 0.00 | | | 0.5 | 2.28 | 0.28 | 0.04 | 0.00 | 0.00 | Backward differences (start from last row): * Δf (backward) [ \begin{aligned} Δf_4 &= f_4 - f_3 = 2.28 - 2.00 = 0.28 \ Δf_3 &= f_3 - f_2 = 2.00 - 1.76 = 0.24 \ Δf_2 &= f_2 - f_1 = 1.76 - 1.56 = 0.20 \ Δf_1

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