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Chapter1: Functions

1.1Sets of Numbers and Inequalities درس مجاني !

Set definition: union, intersection, belong, subset.

Set of numbers – real (number) line

Set of numbers: Exercise

Inequalities – linear inequality

Rational inequality

Rational Inequality Exercise – Part 1

Rational Inequality Exercise – Part 2

quadratic inequality exercise

absolute functions – absolute inequality

1.2Functions درس مجاني !

constants – Variables – function defination – vertical line test

Domain and range exercises Part (1)

Domain and range exercises Part (2)

Two function equality

Combining Functions (algebra of functions)

Symmetry – even and odd functions

Value of a function

Function Composition

1.3Inverse Functions درس مجاني !

one-to-one functions

Inverse functions

1.4Trigonometric Functions and Their Inverses درس مجاني !

Angle – angle measure (degree , radian)

Trigonometric functions

Trigonometric functions with two familiar triangles

Reference angle and Phythagorous – Relations

sign of trigonometric functions

Trigonometric identity

Graphs of Trigonometric functions

inverse of sine and cosine functions – tan and cotan – sec and csc

Chapter2: Limits and Continuity

2.1Definition of Limit

Tabular and graphical methods

examples on tabular and graphical methods

formal definition (epsilon-delta method)

one-sided limit

examples on one-sided limits part 1

examples on one-sided limits part 2

one-sidedformal definition (epsilon-delta method)

algebra of limits part 1

algebra of limits part 2

algebra of limits part 3

squeeze (sandwich) theorem

Trigonometric functions limits

2.3Limits Involving Infinity

infinite limits

vertical asymptote

limits at infinty

horizontal asymptote

2.4Continuity of Functions

Continuity at a point and Continuous Functions part 1

Continuity at a point and Continuous Functions part 2

Continuity at a point and Continuous Functions part 3

continuity of composite functions

Intermediate value theorem

Chapter3: Continuity Of Functions

3.1The Derivative and Tangent Line Problem

DERIVATIVE AND THE TANGENT

Examples part 1

Examples part 2

Examples part 3

Differentiability

3.2Differentiation Rules

DIFFERENTIATION RULES

DIFFERENTIATION RULES (Continued)

3.3Derivatives Of Trigonometric Functions

DERIVATIVE OF TRIGONOMETRIC FUNCTION

3.4The Chain Rule

Chain Rule (General Power Rule)

Chain Rule (General Trigonometric Functions)

3.5Implicit Differentiation

IMPLICIT DIFFERENTIATION

3.6Higher Order Derivatives

HIGHER ORDER DERIVATIVES

3.7The Derivative Of Inverse Functions

Derivative of Inverse Trigonometric Functions

Chapter4: Applications Of Differentiation

4.1Extrema Of Functions

Absolute extrema

Critical points

Find absolute extrema on close interval using critical points

4.2The Mean Value Theorem

Rolle’s Theorem

“Mean Value Theorem (Lagrange’s Theorem)”

4.3Increasing and Decreasing Functions

Increasing and Decreasing Functions – Monotonic Functions

Increasing and decreasing test

“First derivative test (Finding Local Extrema)”

“Second derivative test (Finding Concavity)”

Point of Inflection

“Second derivative test (Finding Local Extrema)”

4.5Curve Sketching

Curve-Sketching -Exercise part 1

Curve-Sketching -Exercise part 2

Curve-Sketching -Exercise part 3

Slant Asymptote

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Trigonometric identity

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1.4Trigonometric Functions and Their Inverses
Trigonometric identity

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