Differential Calculus Booster with Problems and Solutions for IIT JEE Main and Advanced Rejaul Makshud McGraw Hill PDF
Preview Differential Calculus Booster with Problems and Solutions for IIT JEE Main and Advanced Rejaul Makshud McGraw Hill
8.5 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 McGraw Hill Education Offices Chennai new York St Louis San Francisco auckland Bogotá caracas Kuala Lumpur Lisbon London Madrid Mexico city Milan Montreal San Juan Santiago Singapore Sydney Tokyo Toronto McGraw Hill Education (India) Private Limited Published by McGraw Hill Education (India) Private Limited, 444/1, Sri Ekambara Naicker Industrial Estate, Alapakkam, Porur, Chennai - 600 116, Tamil Nadu, India 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 or stored in a database or retrieval system without the prior written permission of the publishers. The program listings (if any) may be entered, stored and executed in a computer system, but they may not be reproduced for publication. This edition can be exported from India only by the publishers, McGraw Hill Education (India) Private Limited ISBN (13): 978-93-5260-575-0 ISBN (10): 93-5260-575-6 Information contained in this work has been obtained by McGraw Hill Education (India), from sources believed to be reliable. However, neither McGraw Hill Education (India) nor its authors guarantee the accuracy or completeness of any information published herein, and neither McGraw Hill Education (India) nor its authors shall be responsible for any errors, omissions, or damages arising out of use of this information. This work is published with the understanding that McGraw Hill Education (India) and its authors are supplying information but are not attempting to render engineering or other professional services. If such services are required, the assistance of an appropriate professional should be sought. Typeset at Bharati Composers, D-6/159, Sector-VI, Rohini, Delhi 110 085, and text and cover printed at Cover Designer: Creative Designer Visit us at: www.mheducation.co.in 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
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