SRM University 2007 B.Tech Food Process Engineering FINITE DIFFERENCE AND INTERPOLATION - Question Paper

MA 252
UNIT – II
FINITE DIFFERENCE AND INTERPOLATION

PART – A
1. Define Shifting operator and inverse shifting operator
2. Define averaging operator
3. Define differential operator.
4. Derive the relation ranging from ? and E?
5. What is the relation ranging from E and ?
6. What is the relation ranging from E and ?
7. Derive the relation ranging from E and ?
8. Prove that D =
9. Find f (x) from the table beneath also obtain f (7)
X : 0 1 2 3 4 5 6
F (x) : -1 3 19 53 111 199 323
10. Define Reciprocal factorial polynomial
11. Find the forward differences of
12. Evaluate ?n (eax+b)
13. Evaluate ?n [ Sin (ax + b) ]
14. Evaluate ? log f (x)
15. Evaluate ?(tan-1 x)
16. show that E1/2 = ?
17. Calculate ?4 y3 if y3 = 2, y4 = -6, y5 = 8, y6 = nine and y7 = 17
18. Find the missing value from the subsequent table.
X : 2 3 4 5 6
Y : 45.0 49.2 54.1 - 67.4
19. Define interpolation and extrapolation.

20. Form the divided difference table for the subsequent data:
X : -2 0 3 5 7 8
F(x) : -792 108 -72 48 -144 -252

PART – B

1. Express f(x) = x3 – 3x2 + 5x + seven in terms of factorial polynomial taking h = two and obtain its differences

2. Represent the function f(x) = x4 – 12x3 + 24x2 – 30x + nine and its successive differences in
factorial notation where h = 1.
3. Give the subsequent
X : 0 0.1 0.2 0.3 0.4
ex : one 1.1052 1.2214 1.3499 1.4918
obtain the value of y = ex when x= 0.38
4. Fine the expectation of life age 32 from the subsequent data:
Age : 10 15 20 25 30 35
Expectation of
Life : 35.3 32.4 29.2 26.1 23.2 20.5
5. The subsequent table provide the corresponding values of x and y. Prepare a forward difference table express y as a function of x. Also find y when x = 2.5
X : 0 1 2 3 4
Y : 7 10 13 22 43
6. Fine the value of e1.85, provided e1.7 = 5.4739, e1.8 = 6.0496, e1.9=6.6859
e2.0 = 7.3891, e2.1 = 8.1662, e2.2 = 9.0250, e2.3 = 9.9742

7. Estimate the production for 1964 and 1966 from the subsequent data.
Year : 1961 1962 1963 1964 1965 1966 1967
Production : 200 220 260 - 350 - 430


8. Find the cubic polynomial which takes the subsequent values
X : 0 1 2 3
F (x) : 1 2 1 10
Hence evaluate f (4) using Newton’s forward formula
9. In the table consecutive terms . obtain the 1st and 10th terms of the series;
X : 3 4 5 6 7 8 nine
Y : 4.8 8.4 14.5 23.6 36.2 52.8 73.9
10. Using Newton’s divided difference formula, obtain the values of f (2), f (8) and f (15) provided the subsequent table.
X : 4 5 7 10 11 13
F(x) : 48 100 294 900 1210 2028


11. From the subsequent table obtain f(x) and hence f(6) using Lagranges interpolation formula.
X : 1 2 7 8
F(x) : 1 5 5 4
12. The subsequent table provide identical relation ranging from steam pressure and temperature obtain the pressure at temperature 372.1o
T : 361? 367? 378? 387? 399?
P : 154.9 167.9 191.0 212.5 244.2
13. Using Lagrange’s interpolation formula, obtain the value corresponding to x = 10 from the subsequent table
X : 5 6 9 11
Y: 12 13 14 16
14. Using Lagrange’s interpolation formula, obtain the form of the function f (x) provided that
X : 0 2 3 6
F(x) : 659 705 729 804
15. Apply Lagrange’s formula to obtain f(x) from the subsequent data;
X : 0 1 4 5
F(x) : 4 3 24 39
16. The subsequent table provide certain corresponding values of x and log10x. calculate the value of log10323.5 by using Lagrange’ s interpolation
X : 321.0 322.8 324.2 325.0
Log10x : 2.50651 2.50893 2.51081 2.51188

17. From the data provided below, obtain the value of x when y = 13.5
X : 93.0 96.2 100.0 104.2 108.7
Y : 11.38 12.80 14.70 17.07 19.91
18. Find the age corresponding to the annuity value 13.6 provided the table
Age (x) : 35 40 45 50
Annuity value (y) : 14.9 14.1 13.3 12.5

Earning:   Approval pending.