Limits and continuity videos

Limits intro

Estimating limit values from graphs

Unbounded limits

Connecting limits and graphical behavior

One-sided limits from graphs

One-sided limits from graphs: asymptote

Estimating limits from tables

Approximating limits using tables

One-sided limits from tables

Limit properties

Limits of combined functions: piecewise functions

Limits of combined functions

Theorem for limits of composite functions

Theorem for limits of composite functions: when conditions aren't met

Limits of composite functions: internal limit doesn't exist

Limits of composite functions: external limit doesn't exist

Limits by direct substitution

Limits of trigonometric functions

Undefined limits by direct substitution

Limits of piecewise functions

Limits of piecewise functions: absolute value

Limits by factoring

Trig limit using Pythagorean identity

Limits by rationalizing

Trig limit using double angle identity

Strategy in finding limits

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

Squeeze theorem intro

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

Continuity at a point

Worked example: point where a function is continuous

Worked example: Continuity at a point (graphical)

Worked example: point where a function isn't continuous

Types of discontinuities

Continuity over an interval

Functions continuous at specific x-values

Functions continuous on all real numbers

Removing discontinuities (rationalization)

Removing discontinuities (factoring)

Introduction to infinite limits

Infinite limits and asymptotes

Analyzing unbounded limits: mixed function

Analyzing unbounded limits: rational function

Limits at infinity of quotients (Part 1)

Functions with same limit at infinity

Introduction to limits at infinity

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)

Intermediate value theorem

Worked example: using the intermediate value theorem

Justification with the intermediate value theorem: table

Justification with the intermediate value theorem: equation