**ISBN:**9781259003530**Authors:**Vinay Kumar

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**Author:** Vinay Kumar

**Language:** English

**Length (Pages):** 728 Pages

**Publisher: **Tata McGraw - Hill

**Publication Year** 2012

**Edition:**1stEdition

**Exam:**

**ISBN:** 9781259003530

Table of Contents

1. Limit

Introduction

Concept of Infinity

Theorems on Limits

One-sided limits

determinate and Indeterminate Forms

Factorisation and Cancellation of Common Factors

Rationalization

Limit Using Exapnasion Series of Functions

Standard of Limits

Algebra of limits

Limits when (Some function)

Asymptotes

Limits of a Sequence

Limits of Forms

Sandwich Theorem / Squeeze Play Theorem

L'Hospital's Rule

Geometerical Limits

Miscellaneous Limits

Target Problems

Things to Remember

Exercises

Answers

2. Continuity of Functions

Definition of Continuity

Continuity in an Interval

Classification of Discontinuity

Algebra of Continous Functions

Properties of Functions Continous on a Closed Interval

Intermediate Value Theorem

Target Problems

Things to Remember

Exercises

Answers

3. Differentiability

Introduction

Differentiability

Reasons of Non-differentiability

Relation between Continuity and Differentiability

Derivability at Endpoints

Differentiability over an interval

Alternative limit form of the Derivative

Derivatives of Higher Order

Algebra of Differentiable Functions

Functional Equations

Target Problems

Things to Remember

Exercises

Answers

4. Methods of Differentiation

Introduction

Derivative using First principle (ab initio) Method

Derivative of Standard Functions

Rules of Differentiation

The Chain Rule

Logarithmic Differentiation

Derivative of Inverse Functions

Parametric Differentiation

Differentiation of Implicit Functions

Differentiation by Trigonometric Substitution

Derivatives of Higher Order

Successive Differentiation

Derivative of a Determinant

Properties of Derivative

L'Hospital Rule

Target Problems

Things to Remember

Exercises

Answers

5. Tangent and Normal

Introduction

Rate Measurement

Approximation

Error

Tangent and Normal

Angle of Intersection

Common Tangents

Length of Tangent

Target Problems

Things to Remember

Exercises

Answers

6. Monotonicity

Definitions

Monotonicity over an interval

Critical Point

Intervals of Monotonicity

Monotonicity in Parametric Functions

Algebra of Monotonous Functions

Proving Inequalities

Concavity and Point of Inflection

Target Problems

Things to Remember

Exercises

Answers

7. Maxima and Minima

Introduction

Concept of Local Maxima and Local Minima

Fermat Theorem

The First Derivative Test

The First Derivative Procedure for Sketching the Graph of a Continous Function

Second Derivative Test

Higher Order Derivative Test

Extrema of Parametric Functions

Operations on Functions having points of Extrema

Global Maximum and Minimum

Boundedness

Algebra of Global Extrema

Miscellaneous Methods

Optimisation Problems

Asymptotes

Points of Inflection

Curve Sketching

Isolation of Roots

Rolle's Theorem

Deductions of Rolle's Theorem

Lagrange's mean Value Theorem

Corollaries of LMVT

Related Inequalities

Cauchy's Mean Value Theorem

Target Problems

Things to Remember

Exercises

Answers

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