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(Requires calculus)a) Show that if f(x) and g(x) are

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen ISBN: 9780073383095 37

Solution for problem 62E Chapter 3.2

Discrete Mathematics and Its Applications | 7th Edition

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Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

Discrete Mathematics and Its Applications | 7th Edition

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Problem 62E

Problem 62E

(Requires calculus)

a)     Show that if f(x) and g(x) are functions such that f(x) is o(g(x)) and c is a constant, then cf(x) is o(g(x)). where (cf)(x) = cf(x).

b)    Show that if f1(x), is f2(x), and g(x) are functions such that f1(x) is o(g(x)) and f2(x) is o(g(x)), then (f1 + f2)(x) is o(g(x)), where (f1 + f2)(x) = f1(x) + f2(x).

Step-by-Step Solution:

Solution;

Step 1 ;

(a) In this problem given that are function.

and also is  and c is constant.

Then we have to prove that

consider is

Then this can be written as

 where  is some constant and also

Multiply both side by constant

.’.

Hence  is  for some constant .

Step 2 of 2

Chapter 3.2, Problem 62E is Solved
Textbook: Discrete Mathematics and Its Applications
Edition: 7
Author: Kenneth Rosen
ISBN: 9780073383095

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(Requires calculus)a) Show that if f(x) and g(x) are