Answer to Question #60691 in Math for esita

Question

8. a) Find the value of )5( f′ from the following table
(3)
x 0 0.5 1 1.5 2
f(x) 1.0 1.75 3 4.75 7
x 4 7 10 12
y –1 1 2 4
x 0 2 3 4 7 9
f(x) 4 26 58 112 466 922
5
b) Find the value of the constants c ,a in the numerical differentiation formula ,b
y x( ) ay x( )h by x( ) cy x( )h ′
i = i − + i + i +
such that the method is of highest possible order. Derive the corresponding Richardson
extrapolation scheme. (3)
c) Using Stirling’s formula find the number of persons at age 35 years, given
y 512, y 439, y 346, y 243 20 = 30 = 40 = 50 =
where, x
y represents the number of persons at age x years in a life table.