Transcription of Continuity and Differentiability 31.12.08 - NCERT
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Continuity and Differentiability 31.12.08 - NCERT
The whole of science is nothing more than a refinementof everyday thinking. ALBERT EINSTEIN IntroductionThis chapter is essentially a continuation of our study ofdifferentiation of functions in Class XI. We had learnt todifferentiate certain functions like polynomial functions andtrigonometric functions. In this chapter , we introduce thevery important concepts of Continuity , Differentiability andrelations between them. We will also learn differentiationof inverse trigonometric functions. Further, we introduce anew class of functions called exponential and logarithmicfunctions. These functions lead to powerful techniques ofdifferentiation. We illustrate certain geometrically obviousconditions through differential calculus. In the process, wewill learn some fundamental theorems in this ContinuityWe start the section with two informal examples to get a feel of Continuity . Considerthe function1,if0()2,if0xfxx = > This function is of course defined at everypoint of the real line.
Chapter 5 CONTINUITY AND DIFFERENTIABILITY Sir Issac Newton (1642-1727) Fig 5.1 148 MATHEMATICS 0.001, the value of the function is 2. Using the language of left and right hand limits, we may say that the left (respectively right) hand limit of f at 0 is 1 (respectively 2). In particular the left and right hand limits do not coincide. We also ...
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