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Varun Kumar, Lovely Professional University Unit 8: Continuity

Unit 8: Continuity Notes

CONTENTS
Objectives
Introduction
8.1 Continuity at a Point
8.1.1 Continuity of Special Functions

8.1.2 Continuity from the Left and Right
8.1.3 Continuity at an End Point
8.1.4 Continuity on an Interval
8.1.5 Properties of Continuous Functions

8.1.6 Properties of Composite Functions
8.2 The Intermediate Value Theorem
8.2.1 Continuous Functions
8.2.2 Discontinuous Functions
8.2.3 Removing Discontinuous Function

8.3 Bisection Method
8.4 Function at a Point
8.4.1 Properties of Continuos Function

8.4.2 Important Result of Constant Function
8.5 Summary
8.6 Keywords
8.7 Self Assessment

8.8 Review Questions
8.9 Further Readings

Objectives

After studying this unit, you will be able to:
Describe the continuity of a function in an interval.

Explain how to use the theorem of continuity of function with the help of different
examples.

Introduction

Let f be a function that is defined for all x in some open interval containing c. Then f is said to be
continuous at x = c under the following conditions:
1. f(c) is defined.

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