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Assignment # 2
MTH603 (Spring 2017)
Total marks: 20
Lectures # 23  28
Due date: 19072017
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Lecture # 23 to Lecture # 28.
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Question#1 Marks 10
Find an equation of a cubic curve which passes through the points
(0, 1), (0, 4), (1, 5) and (2, 6) using Divided Difference Formula.
Question#2 Marks 10
Find interpolation polynomial by Lagrange’s Formula, with the help of following table,
x 1 2 3 5
0 7 26 124
And hence find value of .
Question#3 Marks 10
Find from the following table,
x 1.3 1.6 1.9 2.2 2.5
2.4 2.9 3.2 4.7 6.4
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Toba Bakht :x Maths ki assignment mai ap bohat active rehti hai, assignment ane c pehle hi ning par upload howi hoti hai :P
i ha to upload ki ha na phly kaisy kr skti hn :o huh :p
ban gai assignment ???
Partially ban gayi hae.
Q1 bhi solve karna hae kia?
Total 2 Q karne hain....
nai nai krny 3 hi hain par marks 2 k milny hain r wo knsy hain 2 ye bi nai btana hamein assignment gor se parho
Question#1 Marks 10
Find an equation of a cubic curve which passes through the points
(1, 3), (0, 4), (1, 5) and (2, 6) using Divided Difference Formula.
Solution:
X 
Y 
1^{st} divided diff 
2^{nd} divided diff 
3^{rd} divided diff 
1 
3 





7 


0 
4 

8 



9 

6 
1 
5 

10 



11 


2 
6 



Y_{0}+(x x_{0})[ (Y_{1} Y_{0}) /( x_{1} x_{0})]+ (x x_{0}) (x x_{1}) )[ (Y_{3} Y_{2}) /( x_{2} x_{1})  (Y_{1} Y_{0}) /( x_{1} x_{0})]
3+ (x (1))(7) + (x(1)) (x0) (8) + (x(1)) (x0)(x1)(6)
3+(x+1)(7) +(x+1)(x)(8) + (x+1)(x)(x1)(6)
3  7x 14 + 8x^{2} + 8x + (x^{2}+x)(x1)(6)
3  7x  14 + 8x^{2}+8x +(x^{3}+x^{2} x^{2}x)(6)
3  7x  14+ 8x^{2} + 8x+(6x^{3} 6x^{2} + 6x^{2} +6x)
3  7x – 14 + 8x^{2} +8x  6x^{3}  6 x^{2} + 6x^{2} +6x
6x^{3} +8x^{2} – x 14 Answer
X=4
6*64 +8*16 4 14
384+128414
274
It is right and wrong please help
I solved with example page handout under topic newton's divided difference
Examplle
Find the equation of a cubic curve which passes through the points (4 , 43) , (7 , 83) , (9 ,
327) and (12 , 1053) using Dividing Difference Formula.
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