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Disscuss MTH603 Assignment no 2 due date is 14 July 2014
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MTH603  Numerical Analysis Assignment No. 2 Solution and Discussion Spring 2014 of VirtualUniversity (VU) Due Date: July 14, 2014
Assignment # 2 (Lecture# 23  28) Of MTH603 (Spring 2014)
Maximum Marks: 30
Due Date: 14 July, 2014
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Question: 1 Marks: 5 + 10
Using Lagrange’s interpolation formula, find the value of cos
6
π
using the following table.
Also
estimate the error in the solution.
x 0
4
π
2
π
y x =cos 1 0.7071 0
Question: 2 Marks: 2.5 + 2.5 + 5 + 5
Estimate (2 3. ) d
dx
and (1 3. ) d
dx
, using the following table.
x 1.3 1.5 1.7 1.9 2.1 2.3
y 3.753 3.523 3.333 1.9922 1.5442 1.2969
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check this if error then accurate this
SINCE X=2.3 OCCURS AT THE END OF THE TABLE,SO WE WILL USE BACKWARD DIFFERENCE FORMULA for derivatives
The backward difference table for the given data is given below
X 
F(x) 
Δy 
y 
y 
y 
y 
1.3 
3.753 





1.5 
3.523 
0.5 




1.7 
3.333 
0.1900 
0.3100 



1.9 
1.9922 
1.3400 
1.1500 
1.4600 


2.1 
1.5442 
0.4480 
0.8920 
2.0420 
3.5020 

2.3 
1.2964 
0.2773 
0.1707 
0.7213 
2.7633 
6.2653 
NOW FOR
SINCE 1.3 appear at the beginning of the table so we will use forward difference formula for which table is given below
X 
F(x) 
Δf(x) 
f(x) 
f(x) 
f(x) 
f(x) 
1.3 
3.753 





1.5 
3.523 
0.5 




1.7 
3.333 
0.1900 
0.3100 



1.9 
1.9922 
1.3400 
1.1500 
1.4600 


2.1 
1.5442 
0.4480 
0.8920 
2.0420 
3.5020 

2.3 
1.2964 
0.2773 
0.1707 
0.7213 
2.7633 
6.2653 
Using the forward difference formula
=
=
==5.8270
is ka table ghalat hai...........
g 0.04 ki jaga 0.4 likha hua hy
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