Calculus I (Math 264) By N.P.Bali, P.N.Gupta

Calculus I (Math 264) By N.P.Bali, P.N.Gupta
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Calculus I (Math 264) By N.P.Bali, P.N.Gupta

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Publisher: Laxmi Publications
ISBN: 9789351380177
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Preface ....................................................................................................................................... v Syllabus ............................................................................................................................ vi vii
1
LIMITS AND CONTINUITY
1 46
1.1 Definition of Limit .................................................................................................. 2 1.2 Basic Limit Theorem ...................................................................................................... 7 1.3 One Sided Limits .......................................................................................................... 18 1.4 Infinite Limits and Limits at Infinity .......................................................................... 23 1.5 Continuity ..................................................................................................................... 29 1.6 The Intermediate Value Theorem and its Applications ............................................. 36 Unit Exercise .......................................................................................................................... 42 Summary ............................................................................................................................... 45
2
DERIVATIVES
47 111
2.1 Definition of Derivative ................................................................................................ 47 2.2 Properties of Derivatives .............................................................................................. 55 2.3 Derivative of Functions Polynomial, Rational, Trigonometric, Exponential, Logarithmic and Hyperbolic Functions ...................................................................... 62 2.4 The Chain Rule ............................................................................................................. 86 2.5 Higher Order Derivatives ............................................................................................. 91 2.6 Implicit Differentiation ................................................................................................. 96 2.7 Tangent and Normal Lines ......................................................................................... 101 Unit Exercise ........................................................................................................................ 106 Summary .............................................................................................................................. 110
3 3.1 3.2 3.3 3.4 3.5
APPLICATIONS OF D ERIVATIVES
112 171
Rolle s Theorem, the Mean Value Theorem, and Their Applications ....................... 112 Monotonic Functions ................................................................................................... 124 Extreme Values of Functions ..................................................................................... 132 The First and Second Derivative Tests ...................................................................... 135 Applications to Extreme Values and Related Rates .................................................. 142