Numerical Analysis (ISS Statistics Paper I (Old Subjective Pattern)): Questions 1 - 7 of 21

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Question number: 1

» Numerical Analysis » Interpolation Formulae » Lagrange

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

Equation

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

Equation

Equation

Equation

Equation

Question number: 2

» Numerical Analysis » Interpolation Formulae » Lagrange

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

Equation

Equation<span class="more">… (1 more words) …</span>

Question number: 3

» Numerical Analysis » Numerical Integration

Appeared in Year: 2013

Essay Question▾

Describe in Detail

Evaluate the following by taking seven ordinates of the integrand:

Equation

Explanation

The seven ordinates of the integrand using Simpson’s rule is

Equation

Where h = 1/6 (b-a) and y k =f (a + kh) for k = 0, 1, 2, 3, 4, 5, 6

Here, b = 1, a = 0, h = 1/6, f (x) = Equation

Equation

Equation

Equation<span class="more">… (10 more words) …</span>

Question number: 4

» Numerical Analysis » Summation Formula » Euler-Maclaurin's

Appeared in Year: 2015

Essay Question▾

Describe in Detail

By using Euler-Maclaurin formula, find the sum

Equation

Explanation

The Euler-Maclaurin formula is

Equation

where

Equation

Given the equation

Equation

Equation

Equation

Question number: 5

» Numerical Analysis » Inverse Interpolation

Appeared in Year: 2015

Essay Question▾

Describe in Detail

Compute the value of Equation by Simpson’s 1/3 rd rule. Given that ln4.0 = 1.39, ln4.2 = 1.43, ln4.4 = 1.48, ln4.6 = 1.53, ln4.8 = 1.57, ln5.0 = 1.61, ln5.2 = 1.65

Explanation

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

Equation

Where h = 1/6 (b-a) and y k =f (a + kh) for k = 0, 1, 2, 3, 4, 5, 6

Here, b = 5.2, a = 4, h = 0.2, f (x) = Equation lnx

Equation<span class="more">… (12 more words) …</span>

Question number: 6

» Numerical Analysis » Inverse Interpolation

Appeared in Year: 2014

Essay Question▾

Describe in Detail

Given the following values of the function y = f (x); evaluate f (4) and also find x for which f (x) = 25.

f (1) = 10, f (2) = 15, f (3) = 42.

Explanation

Given that y = f (x), So

x 1 2 3 4

y 10 15 42?

To find the missing value, we use binomial expansion method. Here 3 values are known, we would take third order finite difference zero. Thus,

Equation

Equation

Equation

Equation

Second question is that if we… (22 more words) …

Question number: 7

» Numerical Analysis » Interpolation Formulae » Lagrange

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

Equation

Given that a = 3, b = 7, c = 9, d = 10 and f (a) =168, f (b) =120, f (c) =72, f (d) =63

Find x = 6, the values of f (x) =?

Equation

Equation

Equation

Equation

Equation

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