determine dominant term and big O for the functions ### Mathematical Functions Represented in TableThe image displays a portion of a table with mathematical expressions in each row, indicating different functions. This can be used within educational content to demonstrate how to compare or evaluate different mathematical expressions based on their growth rates or computational complexity.#### Functions1. **Function 1:** \( 0.01n + 100n^2 \) - This function is a quadratic expression with the dominant term \( 100n^2 \), suggesting that its growth rate is driven primarily by this quadratic term.2. **Function 2:** \( 2n + n^{0.5} + 0.5n^{1.25} \) - This function is a combination of terms with different exponents. The terms include a linear component \( 2n \), a square root component \( n^{0.5} \), and a fractional power component \( 0.5n^{1.25} \).3. **Function 3:** \( 0.01n \log_2 n + n(\log_2 n)^2 \) - This function involves logarithmic components and can be analyzed in terms of complexity involving logarithms. The terms include a linear-logarithmic component \( 0.01n \log_2 n \) and a quadratic-logarithmic component \( n(\log_2 n)^2 \).Each row of the table seems to be centered around comparing or evaluating these functions, potentially for analyzing computational complexity or efficiency in algorithm design. Note that the specific purpose of these functions would depend on their context within the curriculum or lesson.

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determine dominant term and big O for the functions

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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determine dominant term and big O for the functions

### Mathematical Functions Represented in Table

The image displays a portion of a table with mathematical expressions in each row, indicating different functions. This can be used within educational content to demonstrate how to compare or evaluate different mathematical expressions based on their growth rates or computational complexity.

#### Functions

1. **Function 1:**
\( 0.01n + 100n^2 \)
- This function is a quadratic expression with the dominant term \( 100n^2 \), suggesting that its growth rate is driven primarily by this quadratic term.

2. **Function 2:**
\( 2n + n^{0.5} + 0.5n^{1.25} \)
- This function is a combination of terms with different exponents. The terms include a linear component \( 2n \), a square root component \( n^{0.5} \), and a fractional power component \( 0.5n^{1.25} \).

3. **Function 3:**
\( 0.01n \log_2 n + n(\log_2 n)^2 \)
- This function involves logarithmic components and can be analyzed in terms of complexity involving logarithms. The terms include a linear-logarithmic component \( 0.01n \log_2 n \) and a quadratic-logarithmic component \( n(\log_2 n)^2 \).

Each row of the table seems to be centered around comparing or evaluating these functions, potentially for analyzing computational complexity or efficiency in algorithm design. Note that the specific purpose of these functions would depend on their context within the curriculum or lesson.

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