# (Requires calculus) The two parts of this exercise ## Problem 67E Chapter 3.2

Discrete Mathematics and Its Applications | 7th Edition

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Problem 67E

(Requires calculus) The two parts of this exercise describe the relationship between little-o and big-O notation.

a) Show that if f(x) and, g(x) are functions such that f(x) is o(g(x)), then f(x) is O(g(x)).

b) Show that if f(x) and g(x) are functions such that f(x) is O(g(x)), then it does not necessarily follow that f(x) is o(g(x)).

Step-by-Step Solution:

Step 1:

In this problem, we have to show that the relation between big-O and little-o for the function.

Step 2:

The definition for Big- O:

Let f and g be functions from the real numbers to the real numbers. Then f is O(g) if there are constants c and k

Such that  That means O(g(x)) is the set of all functions with a smaller or the same order of growth as f(x).

Example:     O(x2) = {x2 , 50x +40 , logx,.....}

The definition for little-o:

Let f and g are two functions, and o(g(x)) is the set of all functions with a smaller rate of growth than f(x).

Example:  o(x2) = {50x +40, logx,...}

Step 3 of 4

Step 4 of 4

##### ISBN: 9780073383095

This full solution covers the following key subjects: such, show, functions, necessarily, follow. This expansive textbook survival guide covers 101 chapters, and 4221 solutions. The full step-by-step solution to problem: 67E from chapter: 3.2 was answered by , our top Math solution expert on 06/21/17, 07:45AM. Since the solution to 67E from 3.2 chapter was answered, more than 229 students have viewed the full step-by-step answer. Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095. This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 7th. The answer to “(Requires calculus) The two parts of this exercise describe the relationship between little-o and big-O notation.a) Show that if f(x) and, g(x) are functions such that f(x) is o(g(x)), then f(x) is O(g(x)).________________b) Show that if f(x) and g(x) are functions such that f(x) is O(g(x)), then it does not necessarily follow that f(x) is o(g(x)).” is broken down into a number of easy to follow steps, and 56 words.

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