Trigonometry (11th Edition)
Trigonometry (11th Edition)
11th Edition
ISBN: 9780134217437
Author: Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher: PEARSON
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**Question 7** Consider the recurrence relation: \( T(n) = \begin{cases} c, & \text{if } n = 1 \\ 2T(n-1) + c, & \text{if } n > 1 \end{cases} \) Fill in the blank next to each statement below with T if the statement is True, or with F if the statement is False. - \( T(n) = O(n^3) \) - \( T(n) = \Theta(n^2) \) - \( T(n) = \Theta(2^n) \) - \( T(n) = \omega(n^2) \) **Question 8** Consider the function \( g(n) = 1 + c + c^2 + \ldots + c^n \), where \( c \) is a positive real number greater than 1. Fill in the blank next to each statement below with T if the statement is True, or with F if the statement is False. - \( g(n) = \Theta(1) \) - \( g(n) = \Theta(n) \) - \( g(n) = \Theta(c^n) \)
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Transcribed Image Text:**Question 7** Consider the recurrence relation: \( T(n) = \begin{cases} c, & \text{if } n = 1 \\ 2T(n-1) + c, & \text{if } n > 1 \end{cases} \) Fill in the blank next to each statement below with T if the statement is True, or with F if the statement is False. - \( T(n) = O(n^3) \) - \( T(n) = \Theta(n^2) \) - \( T(n) = \Theta(2^n) \) - \( T(n) = \omega(n^2) \) **Question 8** Consider the function \( g(n) = 1 + c + c^2 + \ldots + c^n \), where \( c \) is a positive real number greater than 1. Fill in the blank next to each statement below with T if the statement is True, or with F if the statement is False. - \( g(n) = \Theta(1) \) - \( g(n) = \Theta(n) \) - \( g(n) = \Theta(c^n) \)
## Question 9 **T(n) =** - **1, if n < 3** - **T(2n/3) + n, if n > 1.** Fill in the blank next to each statement below with T if the statement is True, or with F if the statement is False. 1. \( T(n) = \Theta(n) \) ___ 2. \( T(n) = \Theta(n^3) \) ___ 3. \( T(n) = \Theta(n^2) \) ___ 4. \( T(n) = O(n^2) \) ___
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Transcribed Image Text:## Question 9 **T(n) =** - **1, if n < 3** - **T(2n/3) + n, if n > 1.** Fill in the blank next to each statement below with T if the statement is True, or with F if the statement is False. 1. \( T(n) = \Theta(n) \) ___ 2. \( T(n) = \Theta(n^3) \) ___ 3. \( T(n) = \Theta(n^2) \) ___ 4. \( T(n) = O(n^2) \) ___
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