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 ____ _________ __________ _______ ___ ________ ____ _________ ____.
______ ______ ________ _____ _____ ___ _____ ____ ___ ___.
_______ __________ __________ ________ _______ ____ _________.
______ _____ _________ _____ _______ _____ __________ ________ ________.
____ _____ _____ ________ ________.
__________ ________ ____ _____ __________ ___ _________ ________ _____ ____ _____ __________.
____ ________ ____ __________ _______.
__________ _______ ________ ______ __________ ___ ______ _______ __________.
_______ __________ ________ ___ _________ __________ ______ ________ __________ ____.
_________ _________ ____ ________ _____ ___ _______ _________.
_________ __________ _______ _________ ___.
_______ __________ _________ _________ ____ ________ ________ _________ _______.
_______ ___ _____ ______ _____ _____ ______ _______ _____ ______ ______ ____.
______ _______ ____ __________ __________ _____ _________ ___ _____ _________.
____ _________ ___ ____ ___ ______.
________ ______ __________ ________ ____ _________ ______.
____ ______ ____ __________ _________ _______ ________ ________.
______ ____ _____ ______ ______ __________ ______ _____ _____.
________ _________ _____ ___ ________ __________ ___ __________ __________.
___ ___ ____ _____ ___.
________ ________ _____ ______ _____ ______ ___ __________.
______ _____ _____ _________ _____.
________ ___ ______ __________ ___ ______ ____.
____ __________ ________ ____ __________ ______.
___ __________ _________ _____ _____.
__________ __________ ___ _______ _________ ___ ___ __________ _____.
____ ___ ____ __________ ____ ____ ____ _______ _____.
_______ ________ ________ ________ ___ ________ ___.
_________ __________ __________ ___ _________ ___ ____ ______ ___ ___ _______.
__________ _______ _____ _____ ________ ____ ___ _________ __________.
_______ ___ _________ _____ ________ ___ ___ ________ ________ __________ _____.
_____ ___ ____ ________ ___.
__________ ______ ______ ______ _______ __________ _____ __________ __________ ____ __________.
_______ _____ ______ ___ ______ __________ ________ ___.
__________ ___ _______ ______ _____ _______ _________ ______ ______ _________.
__________ _______ ________ ________ _______.
_____ ______ __________ _________ ____ ___ ___ ____.
_____ __________ __________ ________ ____ ______ ______ ____ ______ ___ __________.
_______ __________ _______ _______ _______ ____ ___.
________ ____ _________ __________.
Get Full Answer on WhatsApp

IGNOU Solved Assignments Assignments Ignou Projects Project Previous Year Solved Exam Papers Notes Notes Sample Question Papers Sample Question Papers

IGNOU NEWS

Assignment Submission Last Date Extended Till 30 June 2026 Click Here★★★IGNOU June 2026 TEE Date Sheet Released Click Here★★★

x	-1	0	1	2
f (x)	3	-4	5	-6