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Mathematical Expression Editor

Introduction: What is a limit?

Stars at Night

Two young mathematicians discuss stars and functions.

Geometric View of Limits

Visual introduction to Limits

Geometric View - One Sided Limits

Visual introduction to One-sided Limits

Analytic View - Tables

We discuss how to use tables to determine limits and the inherent danger to using this method.

Limits: Notation, One-sided Limits, and Formal Definitions

We introduce the notation and formal algebraic definitions for limits.

Limit laws

Equal or not?

Here we see a dialogue where students discuss combining limits with arithmetic.

The limit laws

We give basic laws for working with limits.

Continuity and the Intermediate Value Theorem

Roxy and Yuri like food

Two young mathematicians discuss the eating habits of their cats.

Continuity

The limit of a continuous function at a point is equal to the value of the function at that point.

Left/Right Continuity

The limit of a continuous function at an endpoint to determine continuity at endpoints.

Continuity and Limit Laws

Here we see a consequence of a function being continuous.

Continuity of piecewise functions

Here we use limits to check whether piecewise functions are continuous.

The Intermediate Value Theorem

Here we see a consequence of a function being continuous.

(In)determinate forms

Could it be anything?

Two young mathematicians investigate the arithmetic of large and small numbers.

Limits at Infinity

What does it mean to take a limit “At Infinity”?

What Are Indeterminate Forms?

We introduce indeterminate forms and discuss what makes one form indeterminate compared to another.

Limits of the form zero over zero

We want to evaluate limits for which the Limit Laws do not apply.

Limits of the form nonzero over zero

What can be said about limits that have the form nonzero over zero?

Using limits to detect asymptotes

Zoom out

Two young mathematicians discuss what curves look like when one “zooms out.”

Vertical asymptotes

We explore functions that “shoot to infinity” near certain points.

Horizontal asymptotes

We explore functions that behave like horizontal lines as the input grows without bound.

An application of limits

Some examples of application for limits, such as average and instantaneous rates of change.

Limits and velocity

Two young mathematicians discuss limits and instantaneous velocity.

Instantaneous velocity

We use limits to compute instantaneous velocity.
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