Calculate a bound for the truncation error in approximating

 where  and (fact n) denotes factorial of n

Compute the value of the integral

 by using

Rectangular Rule (ii) Trapezoidal Rule and then (iii) Simpson's 1/3 Rule

Explain each of the following concepts, along with at least one suitable example for each: (i) Fixed-point number representation (ii) round-off error (iii) representation of zero as floating point number (iv) significant digits in a decimal number representation (v) normalized representation of a floating point number (vi) overflow

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.

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

Regula-falsi method (ii) Newton Raphson method (iii) Bisection method (iv) Secant method

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