AP Calculus BC
Course Content
Limits and continuity

About the course

Khan Academy in the classroom

Sal interviews the AP Calculus Lead at College Board

Defining limits and using limit notation

Limits intro

Estimating limit values from graphs

Estimating limit values from graphs

Unbounded limits

Onesided limits from graphs

Onesided limits from graphs: asymptote

Connecting limits and graphical behavior

Estimating limit values from tables

Approximating limits using tables

Estimating limits from tables

Onesided limits from tables

Determining limits using algebraic properties of limits: limit properties

Limit properties

Limits of combined functions

Limits of combined functions: piecewise functions

Limits of composite functions

Determining limits using algebraic properties of limits: direct substitution

Limits by direct substitution

Undefined limits by direct substitution

Limits of trigonometric functions

Limits of piecewise functions

Limits of piecewise functions: absolute value

Determining limits using algebraic manipulation

Limits by factoring

Limits by rationalizing

Trig limit using Pythagorean identity

Trig limit using double angle identity

Selecting procedures for determining limits

Strategy in finding limits

Determining limits using the squeeze theorem

Squeeze theorem intro

Limit of sin(x)/x as x approaches 0

Limit of (1cos(x))/x as x approaches 0

Exploring types of discontinuities

Types of discontinuities

Defining continuity at a point

Continuity at a point

Worked example: Continuity at a point (graphical)

Worked example: point where a function is continuous

Worked example: point where a function isn’t continuous

Confirming continuity over an interval

continuity over an interval

Functions continuous on all real numbers

Functions continuous at specific x values

Removing discontinuities

Removing discontinuities (factoring)

Removing discontinuities (rationalization) (Opens a modal)

Connecting infinite limits and vertical asymptotes

Introduction to infinite limits

Infinite limits and asymptotes

Analyzing unbounded limits: rational function

Analyzing unbounded limits: mixed function

Connecting limits at infinity and horizontal asymptotes

Introduction to limits at infinity

Functions with same limit at infinity

Limits at infinity of quotients (Part 1)

Limits at infinity of quotients (Part 2)

Limits at infinity of quotients with square roots (odd power)

Limits at infinity of quotients with square roots (even power)

Working with the intermediate value theorem

Intermediate value theorem

Worked example: using the intermediate value theorem

Justification with the intermediate calue theorem: table

Justification with the intermediate value theorem: equation

Optional videos

Formal definition of limits Part 1: intuition review

Formal definition of limits Part 2: building the idea

Formal definition of limits Part 3: the definition

Formal definition of limits Part 4: using the definition
Differentiation: definition and basic derivative rules
Differentiation: composite, implicit, and inverse functions
Contextual applications of differentiation
Applying derivatives to analyze functions
Integration and accumulation of change
Differential equations
Applications of integration
Parametric equations, polar coordinates, and vectorvalued functions
Infinite sequences and series
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