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

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