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AP Calculus AB – Limits and Continuity

Elementary Math
Elementary Math – Advanced
Elementary Science
Pre Algebra
Algebra 1
Stories
American History

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Elementary Math
Elementary Math – Advanced
Elementary Science
Pre Algebra
Algebra 1
Stories
American History

Course Content

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Intro to Calculus 1 Lesson

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What kind fo problems led to Calculus

Defining Limits and Using Limit Notations 4 Lessons

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Intro to limits – what is a limit of a function

Left hand and right hand limit of a function

Limit of a function with undefined point

Mathematical definition of limit

Estimating Limit Values from Graphs 4 Lessons

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How to find limit from the graph of a function

How to check if a function has a limit

A function can have values even without a limit

Practice – Find limits from graphs

Estimating Limit values from Tables 1 Lesson

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Practice – Find limit of a function from table of values

Determining Limits Using Algebraic Properties of Limits 6 Lessons

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Computing limits using algebra – overview

Limits of few basic function

Algebraic properties of limits – with addition and subtraction

Algebraic properties of limits – with multiplication and division

Algebraic properties of limits – with radical sign

Practice – Find limits using algebraic properties

Determining Limits Using Algebraic Manipulation 8 Lessons

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Limits of Polynomials as x -> a

Limits of Rational Functions as x -> a

Limits of Rational Functions when you have 0 over 0

Limits of Rational Functions when you have 0 over 0 – concept example

Limits involving Radicals

Limits of piecewise defined functions

Few helpful theorems for limit calculations

Limits of Algebraic functions

Selecting Procedures for Determining Limits 1 Lesson

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Observations and methods to find limits of any functions

Determining Limits Using the Squeeze Theorem

Connecting Multiple Representations of Limits

Exploring Types of Discontinuities

Defining Continuity at a Point and over an Interval

Confirming Continuity over an Interval

Removing Discontinuities

Connecting Infinite Limits and Vertical Asymptotes 2 Lessons

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Understand infinite limits

Infinite limits and vertical asymptotes

Connecting Limits at Infinity and Horizontal Asymptotes 9 Lessons

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Understand limit at infinity – end behavior of a function

Limits at infinity and horizontal asymptotes

Limit laws for limits at infinity

Infinite limits at infinity

Limits of x^n at infinity

Limits of polynomials at infinity

Limits of rational functions at infinity

Limits involving radicals at infinity

End behavior of trigonometric functions

Working with the Intermediate Value Theorem (IVT)

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