Continuity and the IVT

Continuity and the IVT

Gabby and Dustin like food

Two young mathematicians discuss the eating habits of their cats.

Continuity

Continuity is defined by limits.

Continuity of piece-wise functions

Here we use limits to ensure piecewise functions are continuous.

The Intermediate Value Theorem

Here we see a consequence of a function being continuous.

Continuity exercises

Here is an opportunity for you to practice using the definition of continuity.

Extrema and the EVT

Maximums and minimums

Maximums and minimums

On this card, we investigate what is meant by the maxima and minima of a function.

The Extreme Value Theorem

On this card, we will determine the conditions that guarantee a continuous function has an absolute maximum and minimum.

Limits with Infinity

Using limits to detect asymptotes

Zoom Out

Two young mathematicians discuss what curves look like when one ‘‘zooms out.’’

Limits of the form nonzero over zero

We want to solve limits that have the form nonzero over zero.

Vertical asymptotes

We explore functions that ‘‘shoot to infinity’’ at certain points in their domain.

Horizontal asymptotes

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

Limits with infinity exercises

Here is an opportunity for you to practice evaluating limits that involve infinity.

Mixed Limit Exercises

Mixed limit exercises 1

Here is an opportunity for you to practice evaluating many different types of limits.

Mixed limit exercises 2

Here is an opportunity for you to practice evaluating many different types of limits.

Mixed limit exercises 3

Here is an opportunity for you to practice evaluating many different types of limits.

Mixed limit exercises 4

Here is an opportunity for you to practice evaluating many different types of limits.

You can download a Certificate as a record of your successes.