Reg. No._____________________
AMRITA VISHWA VIDYAPEETHAM
Amrita School of Engineering, Bengaluru Campus
B.Tech. Degree Examinations October 2021
19MAT201 – Numerical Methods
Sem/Branch: III B.Tech. CSE
Date: 30-10-2021
CO1
CO2
Duration: 90 min.
Max. marks: 50
Course Outcomes
Understand the different root finding methods in solving nonlinear equations
Understand and apply concept of interpolation and inverse interpolation
Answer all questions
a) Does there exists a real root of the function y = Cot x in the interval ,
?
Justify?
b) Let p(x) = x3 -9x2 + 17x + 6 be the Newton’s divided difference interpolating
polynomial of a continuous function over [-1, 3]. Find the value of y at x = 0 using
Lagrange’s interpolating polynomial. Justify your answer.
1
2
3
4
5
6
7
a) Find an iterative formula to solve the equation 3x1/3 = 0 using Newton-Raphson
method.
b) With the initial guess x = 1 and y = 1, use Newton Raphson method solve the
non-linear system of equation sin x +3 cos x – 2 = 0; Cos x – 2 sin y + 0.2 = 0
Carry out 2 iterations.
[3]
[CO1],
[2]
[CO2]
[3]
[7]
[CO1]
Use Newton’s divided difference formula to find the polynomial for the data f(40) =184,
f(50) = 204, f(60) = 226, f(70) = 250, f(80) = 276, f(90) = 304 ? Hence find f(42) and
f(38).
[7]
[CO2]
Solve the equation f(x) = ln x by the method of false position and secant method taking
initial approximations as 0.5 and 2. Perform 3 iterations in both cases and compare the
results. What is your inference?
[10]
[CO1]
Using fixed point iteration method with initial guess as 2, find the root of the equation x
– sin x –(1/2) = 0, correct to 3 decimal places.
[6]
[CO1]
Using Newton’s second law of motion, find the force at 24 seconds associated with a
particle of mass m, using the data given below:
Time (sec)
0
2
4
8
Distance (mts)
0
8
11
19
[6]
[CO2]
[6]
[CO2]
Use
Lagrange’s
log10 654  2.8156,
log10 661  2.8202.
interpolation
method
to
log10 658  2.8182,
find
log10 656 , given
log10 659  2.8189
that
and