Numerical Analysis-Interpolation Formulae [ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)]: Questions 7 - 13 of 14

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Question number: 7

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

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Appeared in Year: 2011

Essay Question▾

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Use Simpson’s rule with five ordinates to compute an approximation to π with the help of the integration of the function (1 + x 2) -1 from 0 to 1.

Explanation

T he rule of the integrand using Simpson’s rule for five ordinates is

where , n = 5

h= (1 - 0) /5 = 1/5

We divide the range 0 to 1 in five equal part i. e.

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Question number: 8

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

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Appeared in Year: 2012

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An unknown function u x has been tabulated below for some selected values of x. Use Newton’s divided difference formula on these to find an approximate value of u 3:

x

0

2

5

10

u x

3

19

73

223

Explanation

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Question number: 9

» Numerical Analysis » Interpolation Formulae » Lagrange

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Appeared in Year: 2012

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Solve the equation f (x) = 0 by using a suitable interpolation formula on the following values:

x

3

4

5

6

f (x)

-2.8

-1.2

-0.3

1.8

Explanation

To solve the equation f (x) = 0, using Lagrange’s inverse interpolation method

… (203 more words) …

Question number: 10

» Numerical Analysis » Interpolation Formulae » Lagrange

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Appeared in Year: 2015

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Fit the exponential curve y = a + bx to the following data

x: 0 2 4

y: 5.01 10 31.62

Explanation

his is not exponential equation, it is a straight line y = a + bx

S. no

x

y

Xy

x 2

1

0

5.01

0

0

2

2

10

20

4

3

4

31.62

126.48

16

Sum

6

46.63

146.48

20

The normal equations is

Using the table, putting these values in normal equations. We get

Solving these two equations, we get the value of

… (24 more words) …

Question number: 11

» Numerical Analysis » Interpolation Formulae » Newton-Gregory

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Appeared in Year: 2010

Essay Question▾

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Evaluate log e 7 by Simpson’s -1/3rd rule.

Explanation

We get log e 7, when

So, the seven ordinates of the integrand using Simpson’s rule is

Where h = 1/6 (b-a) and y k =f (a + kh) for k = 1,2, 3,4, 5,6, 7

Here, b = 7, a = 1, h = 1, f (x) =

… (67 more words) …

Question number: 12

» Numerical Analysis » Interpolation Formulae » Newton-Gregory

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Appeared in Year: 2010

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Estimate U 2 from the following table:

x

1

2

3

4

5

U x

7

-

13

21

37

Explanation

To find the missing value, we use binomial expansion method. Here 4 values are known, we would take fourth order finite difference zero. Thus,

Here for x = 1, U 0 =7, U 1 =? , U 2 =13, U 3 =21, U 4 =37

Question number: 13

» Numerical Analysis » Interpolation Formulae » Gauss

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Appeared in Year: 2009

Essay Question▾

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Find the value of

by taking 5 subintervals and using the Trapezoidal rule.

Explanation

Let

First divided the interval into 5 subintervals

x

0

1/4

1/2

3/4

1

y

1

16/17

4/5

16/25

½

Here a = 0, b = 1, n = 4, h= (b-a) /n = 1/4

the Trapezoidal rule is

… (1 more words) …

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