# 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

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Appeared in Year: 2013

Essay Question▾

### 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

… (99 more words) …

## Question number: 2

» Numerical Analysis » Interpolation Formulae » Lagrange

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Appeared in Year: 2013

Essay Question▾

### 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

… (171 more words) …

## Question number: 3

» Numerical Analysis » Interpolation Formulae » Lagrange

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Appeared in Year: 2010

Essay Question▾

### 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

… (167 more words) …

## Question number: 4

» Numerical Analysis » Interpolation Formulae » Newton (Dividend Difference)

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Appeared in Year: 2010

Essay Question▾

### 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

… (94 more words) …

## Question number: 5

» Numerical Analysis » Interpolation Formulae » Gauss

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Appeared in Year: 2011

Essay Question▾

### 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

… (63 more words) …

## Question number: 6

» Numerical Analysis » Interpolation Formulae » Lagrange

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Appeared in Year: 2010

Essay Question▾

### 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) …

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