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FUNDAMENTALS OF MATHEMATICS DIFFERENTIAL CALCULUS by Sanjay Mishra

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2

Continuity and Differentiability

CONTINUITY
INTRODUCTION

In ordinary language, continuous means any process, which goes on without interruption or without abrupt changes. In mathematics also the word continuous has much the same meaning i.e., continuous function means continuous arrangement of ordered pairs, which further means sufficiently small change in one variable leads to an infinitesimally small change in other variable.

We know that function f is defined as a machine that takes an input c and produces an output f(c). If it is a good machine (a continuous one) a small variation in input must result into a correspondingly small variation in output i.e., a continuous function f(x) produces f(x) nearf(c) as x is taken near to c. For example ...

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