paper - iv - Acharya Nagarjuna University

III B.A./B.Sc. Mathematics
4
Paper IV (Elective -1) - Curriculum
31. If l x
represents the number of persons living at age x in a life table, find as accurately as the data will
permit the value of l 47
. Given that l = 512, l = 439, l = 346, l = 243 .
20 30 40 50
32. Apply Gauss forward formula to find the value of u 9
if u = 14; u = 24; u = 32; u = 40 .
0 4 8 16
33. Given that 12500 = 111⋅ 803399; 12510 = 111⋅ 848111; 12520 = 111⋅892806;
12530 = 111⋅ 937483. Show by Gauss backward formula that 12516 = 111⋅ 874930 .
34. Use Stirling’s formula to find y 28
, given y = 49225, y = 48316, y = 47236, y = 45926,
y 40
= 44306 .
20 25 30 35
35. Given y = 24, y = 32, y = 35, y = 40,find y 25
by Bessel’s formula.
20 24 28 32
36. By means of Newton’s divided difference formula, find the value f () 8 and f ( 15)
from the following
table :
x : 4 5 7 10 11 13
f ( x): 48 100 294 900 1210 2028
37. Using the Newton’s divided difference formula, find a polynomial function satisfying the following data.
x : − 4 −1 0 2 5
f ( x): 1245 33 5 9 1335
38. Using Lagranges interpolation formula find y at x = 301.
x : 300 304 305 307
y: 2⋅4771
24829 ⋅ 24843 ⋅ 24871 ⋅
39. By Lagrange’s interpolation formula, find the form of the function given by
x : 0 1 2 3 4
f ( x): 3 6 11 18 27
1 1 ⎡1
1 ⎤
40. Using Lagrange’s formula, prove that y0 = ( y1+ y− 1) − y3 − y1 − y
1−
y
3
2 8 ⎣
⎢ ( ) (
− −
)
2 2 ⎦
⎥ .
41. Find the least square line for the data points ( −110 , ),( 0, 9),( 17 , ),( 2, 5),( 3, 4),( 4, 3),( 5, 0 ) and ( 6, − 1)
.
42. Find the least square power function of the form y = ax b for the data.
xi
1 2 3 4
yi
3 12 21 35
43. Fit a second degree parabola to the following data :
x : 0 1 2 3 4
y: 1 18 ⋅ 13 ⋅ 25 ⋅ 63 ⋅