Table Of Content8.5 x 11 inch
Differential Calculus Booster JEE main & Adv
11 March 2017 11:05:32 AM
Differential Calculus
Booster
with Problems & Solutions
JEE
Main and Advanced
About the Author
REJAUL MAKSHUD (RM)
Post Graduated from Calcutta University in PURE MATHEMATICS.
Presently, he trains IIT Aspirants at RACE IIT Academy, Jamshedpur.
Differential Calculus
Booster
with Problems & Solutions
JEE
Main and Advanced
Rejaul Makshud
M. Sc. (Calcutta University, Kolkata)
McGraw Hill Education (India) Private Limited
chennai
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Differential Calculus Booster
Copyright © 2017, McGraw Hill Education (India) Private Limited.
No part of this publication may be reproduced or distributed in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise
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ISBN (13): 978-93-5260-575-0
ISBN (10): 93-5260-575-6
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Dedicated to
My Beloved Mom and Dad
Preface
DIFFERENTIAL CALCULUS BOOSTER with Problems & Solutions for JEE Main and Advanced is meant for aspirants
preparing for the entrance examinations of different technical institutions, especially NIT/IIT/BITSAT/IISc. In writing this
book, I have drawn heavily from my long teaching experience at National Level Institutes. After many years of teaching I
have realised the need of designing a book that will help the readers to build their base, improve their level of mathemati-
cal concepts and enjoy the subject.
This book is designed keeping in view the new pattern of questions asked in JEE Main and Advanced Exams. It has
nine chapters. Each chapter has the concept booster followed by a large number of exercises with the exact solutions to
the problems as given below:
Level - I : Problems based on Fundamentals
Level - II : Mixed Problems (Objective Type Questions)
Level - III : Problems for JEE Advanced
Level - IV : Tougher Problems for JEE Advanced
(0.......9) : Integer Type Questions
Passages : Comprehensive Link Passages
Matching : Matrix Match
Reasoning : Assertion and Reason
Previous years papers : Questions asked in Previous Years’ IIT-JEE Exams
Remember friends, no problem in mathematics is difficult. Once you understand the concept, they will become easy.
So please don’t jump to exercise problems before you go through the Concept Booster and the objectives. Once you are
confident in the theory part, attempt the exercises. The exercise problems are arranged in a manner that they gradually
require advanced thinking.
I hope this book will help you to build your base, enjoy the subject and improve your confidence to tackle any type of
problem easily and skillfully.
My special thanks goes to Mr. M.P. Singh (IISc. Bangalore), Mr. Yogesh Sindhwani (Head of School, Lancers International
School, Gurugram), Mr. Manoj Kumar (IIT, Delhi), Mr. Nazre Hussain (B.Tech.), Dr. Syed Kashan Ali (MBBS) and Mr.
Shahid Iqbal, who have helped, inspired and motivated me to accomplish this task. As a matter of fact, teaching being the
best learning process, I must thank all my students who inspired me most for writing this book.
I would like to convey my affectionate thanks to my wife, who helped me immensely and my children who bore with
patience my neglect during the period I remained devoted to this book.
I also convey my sincere thanks to Mr Biswajit Das of McGraw Hill Education for publishing this book in such a
beautiful format.
viii Preface
I owe a special debt of gratitude to my father and elder brother, who taught me the first lesson of Mathematics and to
all my learned teachers—Mr. Swapan Halder, Mr. Jadunandan Mishra, Mr. Mahadev Roy and Mr. Dilip Bhattacharya, who
instilled the value of quality teaching in me.
I have tried my best to keep this book error-free. I shall be grateful to the readers for their constructive suggestions
toward the improvement of the book.
Rejaul Makshud
M. Sc. (Calcutta University, Kolkata)
Contents
Preface vii
1. Real Function 1.1–1.95
Basic Concepts of Real Functions 1.1
Algebraic Operation on Domain of a Function 1.2
Range of a Function 1.2
Types of Functions 1.2
Classification of Functions with Respect to its Images 1.12
Inverse Function 1.14
Compostion of Functions 1.14
Even and Odd Functions 1.15
Algebra of Even and Odd Functions 1.15
Even and Odd Extensions of a Function 1.16
Periodic Function 1.16
Functional Equation 1.18
Exercises 1.18
Answers 1.40
Hints and Solutions 1.40
2. Inverse Trigonometric Functions 2.1–2.84
Introduction to Inverse Function 2.1
Inverse Trigonometric Functions 2.1
Graphs of Inverse Trigonometric Functions 2.2
Constant Property 2.4
Conversion of Inverse Trigonometric Functions 2.4
Composition of Trigonometric Functions and its Inverse 2.5
Composition of Inverse Trigonometric Functions and Trigonometric Functions 2.5
Sum of Angles 2.6
Multiple Angles 2.7
More Multiple Angles 2.7
Exercises 2.8
Answers 2.24
Hints and Solutions 2.25
