Continuity and the IVT

1Continuity and the IVT

1.1Gabby and Dustin like food

Two young mathematicians discuss the eating habits of their cats.

1.2Continuity

Continuity is defined by limits.

1.3Continuity of piece-wise functions

Here we use limits to ensure piecewise functions are continuous.

1.4The Intermediate Value Theorem

Here we see a consequence of a function being continuous.

1.5Continuity exercises

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

Extrema and the EVT

2Maximums and minimums

2.1Maximums and minimums

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

2.2The 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

3Using limits to detect asymptotes

3.1Zoom Out

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

3.2Limits of the form nonzero over zero

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

3.3Vertical asymptotes

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

3.4Horizontal asymptotes

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

3.5Limits with infinity exercises

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

Mixed Limit Exercises

3.6Mixed limit exercises 1

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

3.7Mixed limit exercises 2

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

3.8Mixed limit exercises 3

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

3.9Mixed 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.