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# MTH603 Assignment No. 3 Solution and Discussion Spring 2017 Due Date: July 19, 2017

Assignment # 2

MTH603 (Spring 2017)

Total marks: 20
Lectures # 23 - 28
Due date: 19-07-2017

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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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### Replies to This Discussion

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

Solution khn hae?

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

zalmo bna du sol koi tu

zalima Coca cola pela de....

kc ko b nh atii kaya???

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 1st divided diff 2nd divided diff 3rd divided diff -1 3 -7 0 -4 8 9 -6 1 5 -10 -11 2 -6

Y0+(x- x0)[ (Y1- Y0) /( x1- x0)]+ (x- x0) (x- x1) )[ (Y3- Y2) /( x2- x1) - (Y1- Y0) /( x1- x0)]

3+    (x- (-1))(-7)                      + (x-(-1)) (x-0)      (8)    +    (x-(-1)) (x-0)(x-1)(-6)

3+(x+1)(-7)     +(x+1)(x)(8)   +   (x+1)(x)(x-1)(-6)

3 - 7x -14        +   8x2 + 8x      + (x2+x)(x-1)(-6)

3 - 7x - 14        +   8x2+8x    +(x3+x2- x2-x)(-6)

3 - 7x - 14+ 8x2 + 8x+(-6x3- 6x2 + 6x2 +6x)

3 - 7x – 14 + 8x2 +8x - 6x3 - 6 x2 + 6x2 +6x

-6x3 +8x2 – x- 14  Answer

X=4

-6*64 +8*16 -4 -14

-384+128-4-14

-274

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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