Numerical Analysis-Interpolation Formulae (ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)): Questions 1 - 6 of 14
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Question number: 1
» Numerical Analysis » Interpolation Formulae » Lagrange
Appeared in Year: 2013
Describe in Detail
Use Simpson’s one-third rule to estimate approximately the area of the cross section of a river 80 feet wide, the depth d (in feet) at a distance x from one bank being given by the following table. :
| x | 0 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 |
| d | 0 | 4 | 7 | 9 | 12 | 15 | 14 | 8 | 3 |
Explanation
T he one-third rule of the integrand using Simpson’s rule is
The area of the cross section of a river 80 feet wide is
Here n = 8, b = 80, a = 0, h= (b-a) /n = 10
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Question number: 2
» Numerical Analysis » Interpolation Formulae » Lagrange
Appeared in Year: 2013
Describe in Detail
Find the missing value in the table by assuming a polynomial form for y:
| X | 0 | 1 | 2 | 3 | 4 |
| y | 1 | 2 | 4 | - | 16 |
Explanation
we have given that there are four values of y is given, then find the missing value of y at x = 3 using Lagrange’s interpolation polynomial because the x values is not equal interval.
The table is
| X | 0 | 1 | 2 | 4 |
| y | 1 | 2 | 4 | 16 |
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Question number: 3
» Numerical Analysis » Interpolation Formulae » Lagrange
Appeared in Year: 2010
Describe in Detail
The observed-values of a function are respectively 168,120,72 and 63 at the four positions 3,7, 9 and 10 of the independent variable. What is the best estimate you can give for the value of the function at the position 6 of the independent variable?
Explanation
Using Lagrange’s formula
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Question number: 4
» Numerical Analysis » Interpolation Formulae » Newton (Dividend Difference)
Appeared in Year: 2010
Describe in Detail
If f (x) =1/x 2, find the divided differences f (a, b) and f (a, b, c).
Explanation
we can write the Newton’s divided difference formulas as
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Question number: 5
» Numerical Analysis » Interpolation Formulae » Gauss
Appeared in Year: 2011
Describe in Detail
Use mathematical induction to prove
Explanation
Let ∆ i define the i th finite difference which is defined as
∆ =E-1 where E is a shift operator that is
E n f x = f x + nh
Then
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Question number: 6
» Numerical Analysis » Interpolation Formulae » Lagrange
Appeared in Year: 2010
Describe in Detail
The following values of the function f (x) for values of x are given:
f (l) = 4, f (2) = 5, f (7) = 5, f (8) = 4.
Find the value of f (6) and also the value of x for which f (x) is maximum or minimum.
Explanation
This is written in the table in this function y = f (x)
| x | 1 | 2 | 7 | 8 |
| y | 4 | 5 | 5 | 4 |
For find x = 6, we use Lagrange’s interpolation polynomial because the x values is not equal interval. There are four values of x which gives the y values. The Lagrange’s interpolation polynomial formula is
… (172 more words) …