Determine whether each of the functions 2n+l and 22n is

Chapter 2, Problem 19E

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QUESTION:

Problem 19E

Determine whether each of the functions 2n+l and 22n is O(2n).

Questions & Answers

QUESTION:

Problem 19E

Determine whether each of the functions 2n+l and 22n is O(2n).

ANSWER:

Solution:

Step 1:

 In this problem we need to determine whether each of the functions and is .

 Note:

 Let us consider f and g are functions from the set of integers to the set of real numbers.

 The estimate value can be said that f(x) is O(g(x)) if there are constants C and k such that

 , where  C > 0 and  x> k.The constants C and k are called the witnesses to the relationship.

  The definition of f(x) is O(g(x)) says that f(x) grows slower than some fixed multiple of g(x) as x grows without bound.

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