Numerical Analysis-Interpolation Formulae (ISS Statistics Paper I (Old Subjective Pattern)): Questions 1 - 6 of 14

Get 1 year subscription: Access detailed explanations (illustrated with images and videos) to 165 questions. Access all new questions we will add tracking exam-pattern and syllabus changes. View Sample Explanation or View Features.

Rs. 550.00 or

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

abf(x)dxh3((y0+yn)+4(y1+y3++yn1)+2(… (139 more words) …

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

yx… (241 more words) …

Question number: 3

» 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

f(x)=(xb)(xc)(xd)(ab)(ac)(ad)f(a)+(xa)(x… (340 more words) …

Question number: 4

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

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

f(a,b)=f(b)f(a)ba

=1b21a2ba

=a2b2a2b2(… (205 more words) …

Question number: 5

» Numerical Analysis » Interpolation Formulae » Gauss

Appeared in Year: 2011

Essay Question▾

Describe in Detail

Use mathematical induction to prove

fx+nh=i=0(ni)ifx

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

fx+nh=Enfx

=(1+)n… (44 more words) …

Question number: 6

» Numerical Analysis » Interpolation Formulae » Lagrange

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… (257 more words) …

Sign In