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# (Requires calculus)a) Show that if f(x) and g(x) are ISBN: 9780073383095 37

## Solution for problem 62E Chapter 3.2

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

##### ISBN: 9780073383095

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