Skip to Main Content
Mathematical Methods by Pearson
book

Mathematical Methods by Pearson

by E. Rukmangadachari
May 2024
Intermediate to advanced content levelIntermediate to advanced
437 pages
17h 41m
English
Pearson India
Content preview from Mathematical Methods by Pearson
A-66 Mathematical Methods
4. (a) We can write the equation x
3
+ x
2
1 = 0 in
the form
22
1
() where () (1)
1
1
(1)1
1
xx x
x
xx x
x
ff==
+
⎡⎤
+=⇒ =
⎢⎥
+
⎣⎦
3/2
1
() (2)
2( 1)
x
x
f =−
+
Since f (x) = x
3
+ x
2
−1 and f (0) = 1 < 0
and f (1) = 1 > 0
there lies a positive root a in (0, 1).
3/2
111
(0) 1, (1) . 1
22
2
( ) 1 for all (0, 1)xx
ff
fe
=− < =− <
′′
⇒<
So, the iteration method is applicable.
Let x
0
= 0.75
1
0
2
1
3
2
4
3
5
4
6
5
11
0.75593
1 1.75
11
0.75465
1 1.75593
11
0.75493
1 1.75465
11
0.75487
1 1.75493
11
0.75488
1 1.75487
11
0.75488
1 1.75488
x
x
x
x
x
x
x
x
x
x
x
x
===
+
== =
+
== =
+
== =
+
== =
+
== =
+
Since x
5
= x
6
up to 4 decimal places the
required positive root a = 0.75488.
(b) f ( x) = cos x xe
x
,
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial

You might also like

Applied Mathematical Methods by Pearson

Applied Mathematical Methods by Pearson

Bhaskar Dasgupta
Mathematical Modelling

Mathematical Modelling

Pramod Belkhode, Prashant Maheshwary, Kanchan Borkar, J.P. Modak

Publisher Resources

ISBN: 9781299446557Publisher Website