By decinnial census, the population of a town was given below

Year (x) : 1971 1981 1991 2001 2011

Population (y): 112 132 158 189 226 (in thousands)

(i) Using Stirling's central difference formula, estimate the population for the year 2006

(ii) Using Newton's forward formula, estimate the population for the year 1992.

(iii) Using Newton's backward formula, estimate the population for the year 1980.

Calculate a bound for the truncation error in approximating

 where  and (fact n) denotes factorial of n

Obtain Approximate the value of (3.7)^-1 using first three terms of Taylor's series expansion.

Perform four iterations (rounded to four decimal places) using

(i) Jacobi Method and

(ii) Gauss-Seidel method,

for the following system of equations

. The exact solution is (1, 2, 3)^T. Which method gives better approximation to the exact solution?

Explain what is the role of interpolation in solving numerical problems?

Find out to how many decimal places the value 22/7 is accurate as an approximation of 3.14159265, where the latter is value of, calculated up to 8 places after decimal?

For the following data develop difference table and find forward differences and backward differences