1. Find the polynomial function that fits the given data points and uses it to evaluate f(1.5). 2. Evaluate the missing terms in a table of x-values and f(x)-values. 3. Find the first term of a series where subsequent terms are 8, 3, 0, -1, 0, etc.

1. Assignment#1
Finite Difference & Interpolation
1.Find the polynomial f(x) , which satisfy the following data and hence find the value of f(1.5).
X
1
2
3
4
5
F(X)
4
13
34
73
136
2.Evaluate the missing terms in the following table:
X
0
1
2
3
4
5
F(X)
0
-8
15
-35
3. Find the first term of the series whose second and subsequent terms are 8, 3, 0, -1, 0,….
4. Evaluate (∆2/E) x3 .
5.Estimate the production of cotton in the year 1995 from the data given below:
Year (x)
1991
1992
1993
1994
1995
1996
1997
Production f(x)
20
23
26
29
----34
45
3
6. Prove that ∆ (1-x)(1-2x)(1-3x) = -36, interval of differencing being unity.
7. Express the following functions in their factorial notation, taking h=1.
(a) f(x)= 2x3 – 3x2 +3x –10 (b) f(x) = x4 –12x3 + 12x2 –30x +9.
8. Find the functions, where first differences are
(a) 9x2 +11x +5 (b) x3 +3x2 +5x +12
9. Compute (i) f(1.38) and (ii) f(1.42) from the table :
X
1.1
1.2
1.3
1.4
F(X)
7.831 8.728 9.697 10.744
10. In an examination the number of candidates who secured marks between certain limits were as follows:
Marks
0-19
20-39
40-59
60-79
80-99
No. of candidates
41
62
65
50
17
Estimate the numbers of candidates getting marks less than 70.
11. Compute f(5) from the given data:
X
2
4
7
9
F(X)
10
26
65
101
12. Use Newtion’s divided difference formula to find (i) f(8) and (ii) f(15) from the table:
X
4
5
7
10
11
13
F(X)
48
100
294
900
1210
2078
13. Find the polynomial of the least degree, which attains the prescribed values at the given points:
X
-2
1
2
4
F(X)
25
-8
-15
-25
14. Compute the value of x, for y= 0.6742 from the table
X
3.5
4
4.8
5.6
Y
0.5441 0.602 0.6812 0.7482
0
.