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2. Functions and Limit
Khyber Pakhtunkhwa Board > Class 12 > Math (
Total Videos: 576
)
All Chapters
Chapter 1: 1. Introduction to Symbolic Package: MAPLE
Chapter 2: 2. Functions and Limit
Chapter 3: 3. Differentiation
Chapter 4: 4. Higher Order Derivatives and Applications
Chapter 5: 5. Differentiation of Vector Functions
Chapter 6: 6.Integration
Chapter 7: 7-Plane Analytic Geometry Straight Line
Chapter 8: 8- Conics-I
Chapter 9: 9-Conics-II
Chapter 10: 10-Differential Equations
Chapter 11: 11-Partial Differentiation
Chapter 12: 12-Introduction to Numerical Methods
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Chapter 2: 2. Functions and Limit (
73 videos
)
  (
Practice Test
)
2.1: 2.1-Functions  (
Practice Test
)
Introduction to Function
More on Introduction to Functions
Problem3-Introduction to Function
Problem4-Introduction to Function
Domain & Range of Binary Relation
Finding Domain and Range of Functions
Finding Domain and Range from the graph of a function
More on Finding Domain and Range from the graph of a function
The Modulus of a Function
2.2: 2.2-Composition of Functions
Composition of a Functions
Problem-Composition of Functions
2.3: 2.3-Inverse of Composition Functions  (
Practice Test
)
Inverse of a Function
More on Inverse of a Functions
Problem-Inverse of a Function
Algebraic Method to find the Inverse Function
Problem-Algebraic Method to find the Inverse Function
2.4: 2.4-Transcendental Functions  (
Practice Test
)
Algebraic Functions
Trigonometric Functions
Operations on Residue Classes Modulo n
Properties of Binary Operations
More on Logarithmic Functions
Law of Change of Base of Logarithm
Problem 1: Law of Change of Base of Logarithm
Product Law of Logarithm
Problem 1: Product Law of Logarithm
Power Law of Logarithm
Problem 1: Power Law of Logarithm
Quotient Law of Logarithm
Problem 1: Quotient Law of Logarithm
Hyperbolic Functions
Explicit and Implicit Functions
Parametric Functions
2.5: 2.5-Graphical Representation of Functions  (
Practice Test
)
Graph of the Exponential Function
Problem1-Graph of the Exponential Function
More on Graph of Exponential Function
Problem1-More on Graph of Exponential Function
Graph of Common Logarithmic Function
Problem1-Graph of Common Logarithmic Function
Graph of Natural Logarithmic Function
Problem1-Graph of Natural Logarithmic Function
Graph of Parametric Equations
Problem1-Graph of Parametric Equations
Graphs of Discontinuous Functions
Problem1-Graphs of Discontinuous Functions
2.6: 2.6-Limiit of a Function  (
Practice Test
)
Depiction of Real Number on Number Line
Trichotomy Property of Inequality
Problem-Trichotomy Property of Inequality
Problem 1: Trichotomy Property of Inequality
Defining Interval
Defining Closed, Open, Half Open and Half Closed Interval
Meaning of the Phrase 'x' Approaches zero, Infinity
Problem-Meaning of the Phrase 'x' Approaches zero, Infinity
Theorems on Limit of Functions
Defining Sequence and Limit of Sequence
Bounded Set and Monotonic Sequence
Convergent and Divergent Sequence
Limit Theorem of Sequence
More on Limit Theorem of Sequence
Concept of a Limit of a Function
Problem-Concept of Limit of a Function
Evaluate Limits of Different Algebraic, Exponential & Trigonometric F
2.7: 2.7-Important Limits  (
Practice Test
)
Method for Evaluating the Limits at Infinity
Problem-Method for Evaluating the Limits at Infinity
Deducting Formulae at Limit Approaches to 0 and infinity
Problem-Deducting Formulae at Limit Approaches to 0 and infinity
2.8: 2.8-Continuous and Discontinuous Functions  (
Practice Test
)
One-Sided Limits
Criterion for Existence of Limit of a Function
Problem1-Criterion for Existence of Limit of a Function
Using graph to estimate Limit
More on Using graph to estimate Limit
Continuity of a Function at a Number
Test Continuity and Discontinuity of a Function at a Point in an Inte
Problem-Test Continuity & Discontinuity of Function at a Point
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