2. Functions and Limit

Chapter 2: 2. Functions and Limit (73 videos)   (Practice Test)

2.1: 2.1-Functions  (Practice Test)

1. Introduction to Function
2. More on Introduction to Functions
3. Problem3-Introduction to Function
4. Problem4-Introduction to Function
5. Domain & Range of Binary Relation
6. Finding Domain and Range of Functions
7. Finding Domain and Range from the graph of a function
8. More on Finding Domain and Range from the graph of a function
9. The Modulus of a Function

2.2: 2.2-Composition of Functions

1. Composition of a Functions
2. Problem-Composition of Functions

2.3: 2.3-Inverse of Composition Functions  (Practice Test)

1. Inverse of a Function
2. More on Inverse of a Functions
3. Problem-Inverse of a Function
4. Algebraic Method to find the Inverse Function
5. Problem-Algebraic Method to find the Inverse Function

2.4: 2.4-Transcendental Functions  (Practice Test)

1. Algebraic Functions
2. Trigonometric Functions
3. Operations on Residue Classes Modulo n
4. Properties of Binary Operations
5. More on Logarithmic Functions
6. Law of Change of Base of Logarithm
7. Problem 1: Law of Change of Base of Logarithm
8. Product Law of Logarithm
9. Problem 1: Product Law of Logarithm
10. Power Law of Logarithm
11. Problem 1: Power Law of Logarithm
12. Quotient Law of Logarithm
13. Problem 1: Quotient Law of Logarithm
14. Hyperbolic Functions
15. Explicit and Implicit Functions
16. Parametric Functions

2.5: 2.5-Graphical Representation of Functions  (Practice Test)

1. Graph of the Exponential Function
2. Problem1-Graph of the Exponential Function
3. More on Graph of Exponential Function
4. Problem1-More on Graph of Exponential Function
5. Graph of Common Logarithmic Function
6. Problem1-Graph of Common Logarithmic Function
7. Graph of Natural Logarithmic Function
8. Problem1-Graph of Natural Logarithmic Function
9. Graph of Parametric Equations
10. Problem1-Graph of Parametric Equations
11. Graphs of Discontinuous Functions
12. Problem1-Graphs of Discontinuous Functions

2.6: 2.6-Limiit of a Function  (Practice Test)

1. Depiction of Real Number on Number Line
2. Trichotomy Property of Inequality
3. Problem-Trichotomy Property of Inequality
4. Problem 1: Trichotomy Property of Inequality
5. Defining Interval
6. Defining Closed, Open, Half Open and Half Closed Interval
7. Meaning of the Phrase 'x' Approaches zero, Infinity
8. Problem-Meaning of the Phrase 'x' Approaches zero, Infinity
9. Theorems on Limit of Functions
10. Defining Sequence and Limit of Sequence
11. Bounded Set and Monotonic Sequence
12. Convergent and Divergent Sequence
13. Limit Theorem of Sequence
14. More on Limit Theorem of Sequence
15. Concept of a Limit of a Function
16. Problem-Concept of Limit of a Function
17. Evaluate Limits of Different Algebraic, Exponential & Trigonometric F

2.7: 2.7-Important Limits  (Practice Test)

1. Method for Evaluating the Limits at Infinity
2. Problem-Method for Evaluating the Limits at Infinity
3. Deducting Formulae at Limit Approaches to 0 and infinity
4. Problem-Deducting Formulae at Limit Approaches to 0 and infinity

2.8: 2.8-Continuous and Discontinuous Functions  (Practice Test)

1. One-Sided Limits
2. Criterion for Existence of Limit of a Function
3. Problem1-Criterion for Existence of Limit of a Function
4. Using graph to estimate Limit
5. More on Using graph to estimate Limit
6. Continuity of a Function at a Number
7. Test Continuity and Discontinuity of a Function at a Point in an Inte
8. Problem-Test Continuity & Discontinuity of Function at a Point