Consider the following incomplete Newton's forward difference table. f(x) A®fi A) fi A® fi A®fi i 4 -3 A D 1 1 3 E 3 4 a – 4 C 4 a 76— а 4 76 i. Find the value of A, B, C, D, and E in terms of a. ii. Use part (i) to show that a = 25. iii. Use Newton's forward difference formula to estimate f(1.5). 1. 3.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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a) Consider the following incomplete Newton's forward difference table.
i
f(x) A@f A( fi A®fi A® fi
1
4
-3
A
1
1
E
3
4
a – 4
C
4
76 – a
a
4
76
i. Find the value of A, B, C, D, and E in terms of a.
ii. Use part (i) to show that a = 25.
iii. Use Newton's forward difference formula to estimate f(1.5).
b) Approximate the integral
r2 tan
-1
dx,
VI+x²
by using
Simpson's rule with 10 sub-intervals in between 0 and 27.
3
c) Evaluate the integral
e" (x + 1)
dx,
V1- x2
using 3-points Gaussian quadrature.
Transcribed Image Text:a) Consider the following incomplete Newton's forward difference table. i f(x) A@f A( fi A®fi A® fi 1 4 -3 A 1 1 E 3 4 a – 4 C 4 76 – a a 4 76 i. Find the value of A, B, C, D, and E in terms of a. ii. Use part (i) to show that a = 25. iii. Use Newton's forward difference formula to estimate f(1.5). b) Approximate the integral r2 tan -1 dx, VI+x² by using Simpson's rule with 10 sub-intervals in between 0 and 27. 3 c) Evaluate the integral e" (x + 1) dx, V1- x2 using 3-points Gaussian quadrature.
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