BCA Semester 4 – Numerical Methods – Unit 1: Solution of Nonlinear Equations (10Hrs.)

Compute the root of equation $x2−5x+6=0$ in the vicinity of $x=5$ using Newton-Raphson method.

Write an algorithm and program to compute root of nonlinear equation using bisection method.

If the true value of π is 3.1415926 and its approximate value is given by 3.1428571. Find the absolute and relative errors.

When would we not use N-R method? Find the root of the equation

$x3−4x+1=0,$

lying in (0, 1) using Bisection method performing 10 iterations.

Define error. Explain the Taxonomy Errors.

Explain absolute and relative error. Find the relative error of number 5.6 if both of its digits are correct.

Write an algorithm and program to compute the root of nonlinear equation using Newton - Raphson method.

On what type of equations Newton's methods can be applicable. Justify.

How can x we use Laterpolation techniques (methods) to approximate the value of the root for the functions whose derivative can't be found? Explain. Write a program to solve $sin\space x - 2x + 1 = 0$ using Bisection method.