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AP Calculus AB – Limits and Continuity

Intro to Calculus
1 Lesson
What kind fo problems led to Calculus
Defining Limits and Using Limit Notations
4 Lessons
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
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
Practice – Find limit of a function from table of values
Determining Limits Using Algebraic Properties of Limits
6 Lessons
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
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
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
Understand infinite limits
Infinite limits and vertical asymptotes
Connecting Limits at Infinity and Horizontal Asymptotes
9 Lessons
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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Practice – Find limits using algebraic properties

AP Calculus AB – Limits and Continuity Determining Limits Using Algebraic Properties of Limits Practice – Find limits using algebraic properties

Questions :

Find the limits of the following functions:

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Find the limits of the following functions:

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Find the limits of the following functions:

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Explanations :

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