Math 12
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1.1 Introduction
1.1 Introduction
1.1.1 Concept of Function
1.1.2 Definition (Function - Domain - Range)
1.1.3 Notation and Value of Function
1.1.4 Graphs of Algebraic Functions
1.1.5 Graphs of Functions defined piece-wise
1.2 Types of Functions
1.2 Types of Functions
1.2.1 Algebraic Functions
1.2.2 Trigonometric Functions
1.2.3 Inverse Trigonometric Functions
1.2.4 Exponential Function
1.2.5 Logarithmic Function
1.2.6 Hyperbolic Functions
1.2.7 Inverse Hyperbolic Functions
1.2.8 Explicit Function
1.2.9 Implicit Function
1.2.10 Even Function
1.2.11 Odd Function
Exercise 1.1
1.3 Cpmposition of Functions and Inverse of a Function
1.3 Cpmposition of Functions and Inverse of a Function
1.3.1 Composition of Functions
1.3.2 Inverse of a Function
1.3.3 Algebraic method to find the Inverse Function
Exercise 1.2
1.4 Limit of s Funtion and Theorems on limits
1.4 Limit of s Funtion and Theorems on limits
1.4.1 Meaning of the phrase x approaches zero
1.4.2 Meaning of the phrase x approaches infinity
1.4.3 Meaning of the phrase x approaches a
1.4.4 Concept of limit of a function
1.4.5 Limit of a Function
1.4.6 Theorems on limits of Functions
1.5 Limits of important Functions
1.5 Limits of important Functions
1.5.3 limit at infinity
1.5.4 Method for Evaluating the limits at Infinity
1.5.7 the sandwitch theorem
Exercise 1.3
1.6 Continuous and Discontinuous Functions
1.6 Continuous and Discontinuous Functions
1.6.1 one-sided Limits
1.6.2 Criterion for Existence of limit of a Function
1.6.3 Continuity of a function at a number
Exercise 1.4
1.7 Graphs
1.7 Graphs
1.7.1 Graph of the Exponential function f(x) = ax
1.7.2 Graph of the Exponential function f(x) = ex
1.7.3 Graph of common Logarithmic Function f(x)=lgx
1.7.4 Graphs of Natural logarithmic Function f(x)=lnx
1.7.5 Graphs of implicit Functions
1.7.5 Graph of parametric Equations
1.7.6 Graphs of Discontinuous Functions
1.7.7 Graphical Solution of the Equations
Exercise 1.5
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