Page 199 - DMTH201_Basic Mathematics-1

Basic Mathematics – I Varun Joshi, Lovely Professional University

Notes Unit 7: Limits

CONTENTS
Objectives
Introduction
7.1 Limits and Function Values
7.1.1 Properties of Limits

7.1.2 Limit of a Difference Quotient
7.1.3 Laws of Limits
7.2 Limits of a Function
7.2.1 Limits of Left and Right Hand

7.3 Tangents and Limits
7.4 The Pinching or Sandwich Theorem
7.5 Infinite Limits

7.6 Basic Theorems of Limits
7.6.1 Limits of Important Functions

7.7 Summary
7.8 Keywords
7.9 Self Assessment
7.10 Review Questions

7.11 Further Readings
Objectives

After studying this unit, you will be able to:
Discuss limits of a function
Explain how to use the basic theorems on limits

Introduction

In the last unit you have studied about functions. In this unit you are going to study limits and
continuity. Let f be a function and let c be a real number such that f(x) is defined for all values

of x near x = c, except possibly at x = c itself. Suppose that whenever x takes values closer and
closer but not equal to c (on both sides of c), the corresponding values of f(x) get very close to and
possibly equal to the same real number L. The values of f(x) can be made arbitrarily close to L by
taking values of x close enough to c, but not equal to c.
The limit of the function f(x) as x approaches c is the number L.
= L

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