Calculus Its Application Chapter 2 Introduction to Limits

-Calculus & It’s Application. Chapter 2 Introduction to Limits 朝陽科技大學 資訊管理系 李麗華 教授

Introduction to Limits • Since 16 century, there were many scientists used calculus-like method to solve problems. However, the inventing of calculus should be credited to Newton and Leibniz. • Newton invented calculus in 1665, however he took more than 20 years to publish his results. Leibniz was thought as the first man who published theory of calculus and the notation he proposed has been used until today. • Calculus application has found in almost every areas, such as speed of blood flows, size of packaging, maximization of the product level. 2

Introduction to Limits • In this chapter, we will introduce the following topics: – Introduction to limits – Continuity – One-sided limits – Limits at infinity – Infinite limits 3

2 -1 Introduction to Limits • 定義 – For any function means that as , gets closer and closer to , Gets closer and closer to – Limit Theorems: If , and are real numbers, then C為常數 7

2 -1 Introduction to Limits • 練習: 8

2 -1 Introduction to Limits • 上台練習: 9

2 -2 Continuity • If the graph of a function has no break, gap, holes, or jumps in them, then this function can be called as a continuous function • If is continuous at , then If then 本定義包含三項要素，即(1) (2) is continuous at . 一定要存在， 必有定義(值)， (3) 12