Calculus 1 : Course in Mathematics for the IIT-JEE and Other Engineering Entrance Examinations

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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