Course
Name
B.tech
Branch
Subject Name with Code
Semester
ME/
Mathematics-iii (Numerical Methods )IBS-304
CE/CSE/ECE/EE
3
Assignment
Unit No.
1
Objective types Questions – Answers (1 Marks each)
Rate of convergence of the Newton-Raphson method is generally __________
a) Linear
b) Quadratic
c) Super-linear
d) Cubic
2. The Newton-Raphson method of finding roots of nonlinear equations falls under the category
of which of the following methods?
a) bracketing
b) open
c) random
d) graphical
1.
3. At which point the iterations in the Newton Raphson method are stopped?
a) When the consecutive iterative values of x are not equal
b) when the consecutive iterative values of x differ by 2 decimal places
c) When the consecutive iterative values of x differ by 3 decimal places
d) when the consecutive iterative values of x are equal
4. What is the source of discretization error in the finite difference method?
a) Numerical error
b) Round-off error
c) Truncation error
d) Modelling error
5. Which is the major error occurring due to the finite difference approximations?
a) Discretization error
b) Round-off error
c) Iteration error
d) Modelling errors
Very Short Questions – Answers (2 Marks each)
1. Define Newton-Raphson method.
2. What do you mean by error and their computations?
3. Define significant digits.
4. What is round off numbers?
5. What is truncation error?
Long Questions- Answers (7 Marks each)
1. Find a positive root of the equation 𝑥𝑒 𝑥 = 1 which lies between 0 and 1.
2. Given that the equation 𝑥 2.2 = 69 has a root below 5 and 8.Use the method of regula falsi to
determine it.
3. The method of iteration to find a positive root, between 0 and 1 of the equation 𝑥𝑒 𝑥 = 1.
4. Find a root of the equation 𝑥𝑠𝑖𝑛𝑥 + 𝑐𝑜𝑠𝑥 = 0.
5. Find the root of the equation 𝑥 = 𝑒 −𝑥 , using the Newton-Raphson method.