CALCULUS 1 : course in mathematics for the iit-jee and other engineering entrance examinations;course in mathematics for the iit-jee

Course in Mathematics: A Lecture-wise Approach is a complete resource that is designed to help students master mathematics for the coveted IIT-JEE, AIEEE, state-level engineering entrance exams and all other state senior secondary exams, in addition to the AISSSCE. This meticulously crafted and designed series reflects the command and authority of the authors on the subject. The series adopts an easy step-by-step approach to make learning mathematics at the senior secondary level a joyful experience. Key Features: Adopts a well-defined, meticulously planned and smartly structured learning approach. Includes lecture-wise tests that help revise each completed lecture. Contains Speed Accuracy Sheets that improve the speed and accuracy of students and help them revise key concepts. Provides innovative tips and tricks that are easy to apply and remember. Includes solved Topic-Wise Question Banks to enhance the comprehension and application of concepts. Table Of Contents: PART A FUNCTIONS Lecture 1 Definitions, Value of Functions Lecture 2 Domain and Range of Real Functions Lecture 3 Algebra of Functions Lecture 4 Mapping of Functions Lecture 5 Test Your Skills PART B LIMITS Lecture 1 Basic Definition, Evaluation of limits (Basic) Lecture 2 Evaluation of Limits Lecture 3 Test Your Skills PART C CONTINUITY Lecture 1 Evaluation of Continuity Lecture 2 Continuous Functions Lecture 3 Test Your Skills PART D DIFFERENTIABILITY Lecture 1 Existence of Derivatives Lecture 2 Test Your Skills PART E Differentiation Lecture 1 Simple Differentiation Lecture 2 Fundamental Theorems Lecture 3 Differentiation of Inverse Function PART F APPLICATIONS OF DERIVATIVES Lecture 1 Monotonic (Increasing and Decreasing) Functions Mean Value Theorem and Approximations Lecture 2 Rolle's Theorem and Rate of Change of Quantities Lecture 3 Tangent and Normal F Lecture 4 Maxima and Minima 1 Lecture 5 Maxima and Minima 2 Lecture 6 Test Your Skills Cover Contents Preface Part A: Functions Lecture 1: Definitions, Value of functions Basic Concepts Notes Unsolved Subjective Problems (XII Board (C.B.S.E/State)): to Grasp the Topic Solve These Problems Answer Solved Objective Problems: Helping Hand Objective Problems: Important Questions with Solutions Solutions Unsolved Objective Problems (Identical Problems for Practice): for Improving Speed with Accuracy Worksheet: To Check the Preparation Level Answer Sheet Hints and Explanations Lecture 2: Domain and Range of Real Functions Basic Concepts Working Rule for finding domain and range of a real function Unsolved Subjective Problems (XII Board (C.B.S.E./State)): to Grasp the topic Solve these Problems Answer Sloved Objective Problems: Helping Hand Objective Problems: Important Questions Questions with Solutions Solutions Unsolved Objective Problems (Identical Problems for Practice): for Improving Speed with Accuracy Worksheet: to Check the Preparation Level Answer Sheet Hints and Explanations Lecture 3: Algebra of Functions Basic Concepts Equality of two Functions Even and Odd Functions Periodic Function Composite Function key skills Unsolved Subjective Problems (XII Board (C.B.S.E./State)): to Grasp the topic Solve these Problems Answer Solved Objective Problems: Helping Hand Objective Problems: Important Questions with Solutions Solutions Unsolved Objective Problems (Identical Problems for Practice): for Improving Speed with Accuracy Worksheet:to Check the Preparation Level Answer Sheet Hints and Explalations Lecture 4: Mapping of Functions Basic Concepts Unsolved Subjective Problems (XII Board (C.B.S.E./State)): to Grasp the topic Solve these Problems Answer Solved Objective Problems: Helping Hand Objective Problems: Important Questions with Solutions Solutions Unsolved Objective Problems (Identical Problems for Practice): for Improving Speed with Accuracy Worksheet: To Check the Preparation Level Answer Sheet Hints and Explanations Lecture 5: Test Your Skills Assertion/Reasoning Assertion and reasoning type Questions Assertion/Reasoning: Solutions Mental Preparation Test Lecturewise Warmup Test 1 Lecturewise Warmup Test 2 Lecturewise Warmup Test 1: Solutions Lecturewise Warmup Test 2: Solutions Answer Part B: Limits Lecture 1: Basic Definition, Evaluation of limits (Basic) Basic Concepts Introduction Definition of Limit Evaluation of Limits (Working Rule) Solved Subjective Problems (XII Board (C.B.S.E./State)): for Better Understanding and Concept Building of the Topic Unsolved Subjective Problems (XII Board (C.B.S.E./State)): to Grasp the topic Solve these Problems Answer Solved Objective Problems: Helping Hand Objective Problems: Important Questions with Solutions Solutions Unsolved Objective Problems (Identical Problems for Practice): for Improving Speed with Accuracy Worksheet: to Check the Preparation level Answer Sheet Hints and Explanations Lecture 2: Evaluation of Limits Basic Concepts Some Important Results Limits Based on 5-Step Rule L-Hospital’s Rule To find the limit by finding L.H. limit and R.H. limit Squeezing Theorem or Sandwich Theorem Points to Remember Solved Subjective Problems (XII Board (C.B.S.E./State)): for Better Understanding and Concept Building of the Topic Unsolved Subjective Problems (XII Board (C.B.S.E./State)): to Grasp the topic Solve these Problems Answer Solved Objective Problems: Helping Hand Objective Problems: Important Questions with Solutions Solutions Unsolved Objective Problems (Identical Problems for Practice): for Improving Speed with Accuracy Worksheet: to Check the Preparation Level Answer Sheet Hints and Explanations Lecture 3: Test Your Skills Mental Preparation Test Lecturewise Warmup Test Lecturewise Warmup Test: Solutions Answer Part C: Continuity Lecture 1: Evaluation of Continuity Basic Concepts Continuity Unsolved Subjective Problems (XII Board (C.B.S.E./State)): to Grasp the topic Solve these Problems Answer Solved Objective Problems: Helping Hand Objective Problems: Important Questions with Solutions Solutions Unsolved Objective Problems (Identical Problems for Practice): for Improving Speed with Accuracy Lecture 2: Continuous Functions Basic Concepts Properties of Continuous functions Algebra of Continuous Functions Points to Remember Solved Subjective Problems (XII Board (C.B.S.E./State)): for Better Understanding and Concept Building of the Topic Unsolved Subjective Problems (XII Board (C.B.S.E./State)): to Grasp the topic Solve these Problems Answer Solved Objective Problems: Helping Hand Objective Problems: Important Questions with Solutions Solutions Unsolved Objective Problems (Identical Problems for Practice): for Improving Speed with Accuracy Worksheet: to Check the Preparation Level Answer Sheet Hints and Explanations Lecture 3: Test Your Skills IIT-Booster Mental Preparation Test Lecturewise Waemup Test Lecturewise Warmup Test: Solutions Answer Part D: Differentiability Lecture 1: Existence of Derivatives Basic Concepts Solved Subjective Problems (XII Board (C.B.S.E./State)): for Better Understanding and Concept Building of the Topic Unsolved Subjective Problems (XII Board (C.B.S.E./State)): to Grasp the topic Solve these Problems Answer Solved Objective Problems: Helping Hand Objective Problems: Important Questions with Solutions Solutions Unsolved Objective Problems (Identical Problems for Practice): for Improving Speed with Accuracy Worksheet: to Check the Preparation Level Answer Sheet Hints and Explanations Lecture 2: Test Your Skills Assertion/Reasoning Assertion and reasoning type Questions Assertion/Reasoning: Solution IIT-Booster Mental Preparation Test Lecturewise Warmup Test Lecturewise Warmup Test: Solutions Answer Part E: Differentiation Lecture 1: Simple Differentiation Basic Concept Derivatives of Some Standrad Functions Fundamenetal Theorems Points to Remember Solved Subjective Problems (XII Board (C.B.S.E./State)): for Better Understanding and Concept Building of the Topic Unsolved Subjective Problems (XII Board (C.B.S.E./State)): to Grasp the topic Solve these Problems Answer Solved Objective Problems: Helping Hand Objective Problems: Important Questions with Solutions Solutions Worksheet: to Check the Preparation Level Answer Sheet Hints and Explanations Lecture 2: Fundamental Theorems Basic Concepts Solved Subjective Problems (XII Board (C.B.S.E./State)): for Better Understanding and Concept Building of the Topic Unsolved Subjective Problems (XII Board (C.B.S.E./State)): to Grasp the topic Solve these Problems Answer Solved Objective Problems: Helping Hand Objective Problems: Important Questions with Solutions Solutions Unsolved Objective Problems (Identical Problems for Practice): for Improving Speed with Accuracy Worksheet: to Check the Preparation Level Answer Sheet Hints and Explanations Lecture 3: Differentiation of Inverse Function Basic Concepts Some Important Differentiations Solved Subjective Problems (XII Board (C.B.S.E./State)): for Better Understanding and Concept Building of the Topic Unsolved Subjective Problems (XII Board (C.B.S.E./State)): to Grasp the topic Solve these Problems Answer Solved Objective Problems: Helping Hand Objective Problems: Important Questions with Solutions Solutions Unsolved Objective Problems (Identical Problems for Practice): for Improving Speed with Accuracy Worksheet: to Check the Preparation Level Answer Sheet Hints and Explanations Answer Part F: Applications of Derivatives Lecture 1: Monotonic (Increasing and Decreasing) Functions, Mean Value Theorem and Approximations Basic Concepts Monotonic Function Largrange’s Mean value Theorem (LMVT) Solved Subjective Problems (XII Board (C.B.S.E./State)): for Better Understanding and Concept Building of the Topic Unsolved Subjective Problems (XII Board (C.B.S.E./State)): to Grasp the topic Solve these Problems Answer Solved Objective Problems: Helping Hand Objective Problems: Important Questions with Solutions Solutions Unsolved Objective Problems (Identical Problems for Practice): for Improving Speed with Accuracy Worksheet: to Check the Preparation Level Answer Sheet Hints and Explanations Lecture 2: Rolle's Theorem and Rate of Change of Quantities Basic Concepts Rolle's Theorem Derivatives as the Rate of Change Solved Subjective Problems (XII Board (C.B.S.E./State)): for Better Understanding and Concept Building of the Topic Unsolved Subjective Problems (XII Board (C.B.S.E./State)): to Grasp the topic Solve these Problems Answer Solved Objective Problems: Helping Hand Objective Problems: Important Questions with Solutions Solutions Unsolved Objective Problems (Identical Problems for Practice): for Improving Speed with Accuracy Worksheet: to Check the Preparation Level Answer Sheet Hints and Explanations Lecture 3: Tangent and Normal Basic Concepts Solved Subjective Problems (XII Board (C.B.S.E./State)): for Better Understanding and Concept Building of the Topic Unsolved Subjective Problems (XII Board (C.B.S.E./State)): to Grasp the topic Solve these Problems Answer Solved Objective Problems: Helping Hand Objective Problems: Important Questions with Solutions Solutions Unsolved Objective Problems (Identical Problems for Practice): for Improving Speed with Accuracy Worksheet: to Check the Preparation Level Answer Sheet Hints and Explanations Lecture 4: Maxima and Minima 1 Basic Concepts Solved Subjective Problems (XII Board (C.B.S.E./State)): for Better Understanding and Concept Building of the Topic Unsolved Subjective Problems (XII Board (C.B.S.E./State)): to Grasp the topic Solve these Problems Answer Solved Objective Problems: Helping Hand Objective Problems: Important Questions with Solutions Solutions Unsolved Objective Problems (Identical Problems for Practice): for Improving Speed with Accuracy Worksheet: to Check the Preparation Level Answer Sheet Hints and Explanations Lecture 5: Maxima and Minima 2 Basic Concepts Points to Remember Solved Subjective Problems (XII Board (C.B.S.E./State)): for Better Understanding and Concept Building of the Topic Unsolved Subjective Problems (XII Board (C.B.S.E./State)): to Grasp the topic Solve these Problems Answer Solved objective Problems: Helping Hand Objective Problems: Important Questions with Solutions Solutions Unsolved Objective Problems (Identical Problems for Practice): for Improving Speed with Accuracy Worksheet: to Check the Preparation Level Answer Sheet Hints and Explanations Lecture 6: Test Your Skills Assertion/Reasoning Assertion and reasoning type Questions Assertion/Reasoning: Solutions Mental Preparation test Lecturewise warmup test Lecturewise Warmup Test: Solutions Answer Calculus-1: Course In Mathematics For The Iit-jee And Other Engineering Entrance Examinations Is Designed To Help Students Master Calculus For The Coveted Iit-jee, Aieee, State-level Engineering Entrance Exams And All Other State Senior Secondary Exams, In Addition To The Aisssce. The Book Adopts A Well-defined, Meticulously Planned And Smartly Structured Learning Approach. It Includes Lecture-wise Tests That Help Revise Each Completed Lecture. It Contains Speed Accuracy Sheets That Improve The Speed And Accuracy Of Students And Help Them Revise Key Concepts. It Also Provides Innovative Tips And Tricks That Are Easy To Apply And Remember And Includes Solved Topic-wise Question Banks To Enhance The Comprehension And Application Of Concepts. This First Volume Deals With Functions, Limits, Continuity, Differentiability And Applications Of Derivatives.