MCSE004- SOLVED ASSIGNMENT 2016-17 IGNOU MCA 5th SEM

1.	(a) If 0.333 is the approximate value of 1/3, then find absolute, relative and percentage errors.
(b) For x = 0.4845 and y = 0.4800,     calculate the value of (x2 – y2)/(x +y) using  normalized floating point arithmetic compare value with the value of (x – y).
2.	(a) Find the real root of equation f(x) = x3 – x – 1 = 0 using Bisection method.
(b) How many iterations of Bisection method are required to be performed, to obtain smallest positive root of x3 – 2x – 5 = 0, correct upto 2 decimal places.
(c) Use Newton's method to find root of the equation x3 – 2x – 5 = 0
3. (a) Use Gauss Elimination to solve 10x1 – 7x2 = 7; -3x1 + 2.099x2 + 6x3 = 3.901; 5x1 – x2 + 5x3 = 6. Correct to six decimal places of significant digit.

(c) Solve the following system of equations using (i) Jacobi Method (ii) Gauss – seidel method x + y – z = 0; - x + 3y = Z, x – 2z = 3, assume the initial solution vector as []T
4. (a) For the given discrete data find the interpolating polynomial using (i) Lagrange's interpolation (ii) Newton Divided difference interfdation

1.	(a) If 0.333 is the approximate value of 1/3, then find absolute, relative and percentage errors.
(b) For x = 0.4845 and y = 0.4800,     calculate the value of (x2 – y2)/(x +y) using  normalized floating point arithmetic compare value with the value of (x – y).
2.	(a) Find the real root of equation f(x) = x3 – x – 1 = 0 using Bisection method.
(b) How many iterations of Bisection method are required to be performed, to obtain smallest positive root of x3 – 2x – 5 = 0, correct upto 2 decimal places.
(c) Use Newton's method to find root of the equation x3 – 2x – 5 = 0
3. (a) Use Gauss Elimination to solve 10x1 – 7x2 = 7; -3x1 + 2.099x2 + 6x3 = 3.901; 5x1 – x2 + 5x3 = 6. Correct to six decimal places of significant digit.

(c) Solve the following system of equations using (i) Jacobi Method (ii) Gauss – seidel method x + y – z = 0; - x + 3y = Z, x – 2z = 3, assume the initial solution vector as []T
4. (a) For the given discrete data find the interpolating polynomial using (i) Lagrange's interpolation (ii) Newton Divided difference interfdation

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