1. Prove that
2. Evaluate the missing term from the following table
X
F(x)
1
2
2
4
3
8
4
----
5
32
6
64
7
128
3. Evaluate the missing term from the following table
X
F(x)
0
0
1
---
2
8
3
15
4
----
5
35
4. Find f(2.8) from the following data
X
F(x)
0
1
1
2
2
11
5. Using the Divided difference formula find
X
F(x)
0
4
3
34
from the following table
2
26
3
58
4
112
7
466
8
668
6. Find the polynomial from the following data
X
F(x)
-1
-1
-2
-9
2
11
4
69
7. compute the value of y at x=1.6 from the following table
X
F(x)
1.0
0.11246
1.5
0.14032
2.0
0.16800
2.5
0.19547
3.0
0.22270
8. Find f(0.9) from the following data
X
F(x)
9. The values of
X
F(x)
0
5
1
14
2
41
4
98
are given below, for different values of x. Find
.5
.5736
.6428
.7071
from this table
.7660
.8192
10. From the following table of sin’s compute
F(x)
0
0.17365
0.34202
0.5
0.64279
11. Find the polynomial from the following data
X
F(x)
0
3
1
6
2
11
3
18
12. Find the interpolating polynomial from the given values, f(-1)=1, f(0)=1, f(1)=1, f(2)=3
by using Lagrange’s interpolation formula.
13. The population of a town in the decennial census was as given bellow. Eestimate the
population for the year 1895, using Newton’s Forward Interpolation formula.
Year
1891
1901
1911
1921
1931
Population
46
66
81
93
103
14.Using the Divided difference formula find
X
F(x)
14. Find
0.62
0.6604918
and
15. Evaluate
from the following table
0.68
0.73363074
0.70
0.7585837
0.75
0.8223167
from the given data: f(0)=7,f(2)=13, f(4)=43, f(6)=145, f(8)=367.
, by simpson’s 1/3rd rule and Trapezoidal rule.
16. Evaluate
, by simpson’s 1/3rd rule taking n=10.
17. Evaluate
by taking n=5.
18. Evaluate
19. Compute
0.73
0.7965858
by simpson’s 1/3rd rule.
x
dx where the interval is
sin x
20. Find the value of
place by (i) Simpson 1/3 rule
(ii) Trapezoidal rule
0,
1 using Trapezoidal rule with h = 1 .
4
2
taking eight equal sub-intervals correct upto 4-decimal