## Example using a sinusoid to model a periodic function

Here we describe the hours of daylight on another planet and find a model to represent it....

From Joshua Helston

Here we describe the hours of daylight on another planet and find a model to represent it....

From Joshua Helston

Here we show that the limit of a difference of sequences is the difference of the limits...

From Joshua Helston

Here we take the limit of a rational expression and provide a rigorous epsilon-N argument...

From Joshua Helston

Here we prove the multiplicative property of zero in a field...

From Joshua Helston

This video has a collection of four limits that were from our exam...

From Joshua Helston

Here we find all roots (some rational, some irrational) of a quartic polynomial...

From Joshua Helston

Here we use induction to establish Bernoulli's inequality that (1+x)^n is less than or equal to 1+nx....

From Joshua Helston

Here we show that a limit does not exist because it does not get arbitrarily close to anything....

From Joshua Helston

Proving a limit using the epsilon-N definition...

From Joshua Helston

Here we show that the limit of a radical of a sequence approaches the radical of the initial limit....

From Joshua Helston

This video details only the discussion involved with finding an appropriate N for an epsilon-N proof of a limit...

From Joshua Helston

This problem has us finding the slope of a line tangent to a particular circle...

From Joshua Helston

Determining the end behavior of the graph of a polynomial function...

From Joshua Helston

Solving a rational equation that simplifies to quadratic: Proportional form, advanced...

From Joshua Helston

Finding x- and y-intercepts given a polynomial function...

From Joshua Helston

Finding the roots of a quadratic equation with leading coefficient greater than 1...

From Joshua Helston

Using a graphing calculator to find the x-intercept(s) and vertex of a quadratic function...

From Joshua Helston

Rewriting a quadratic function to find the vertex of its graph...

From Joshua Helston

Ratios of volumes...

From Joshua Helston

Range of a quadratic function...

From Joshua Helston

Sum and difference identities: Problem type 2...

From Joshua Helston

Sum and difference identities: Problem type 1...

From Joshua Helston

Partial fraction decomposition with repeated linear factors...

From Joshua Helston

Partial fraction decomposition with distinct linear factors...

From Joshua Helston

Partial fraction decomposition with an irreducible quadratic factor...

From Joshua Helston

Graphing an exponential function and its asymptote f(x)=a(b)^x...

From Joshua Helston

Finding the rate or time in a word problem on continuous growth or decay...

From Joshua Helston

Finding a limit by using the limit laws: Problem type 3...

From Joshua Helston

Double angle identities: Problem type 2...

From Joshua Helston

Double angle identities: Problem type 1...

From Joshua Helston

This video explores the power series of e^x and shows that for this function f=f'...

From Joshua Helston

Composition of a trigonometric function and an inverse trigonometric function: Problem type 3...

From Joshua Helston

Finding the time to reach a limit in a word problem on exponential growth or decay...

From Joshua Helston

Finding the initial or final amount in a word problem on exponential growth or decay...

From Joshua Helston

Using cofunction identities...

From Joshua Helston

Composition of a trigonometric function and an inverse trigonometric function: Problem type 2...

From Joshua Helston

Simplifying trigonometric expressions...

From Joshua Helston

Finding a limit by using the limit laws: Problem type 1...

From Joshua Helston

Finding a limit by using the limit laws: Problem type 2...

From Joshua Helston

Here we perform a couple examples of triple sums to familiarize the viewer with the mechanics....

From Joshua Helston

In this video we explore the connection between permutations and combinations via a couple examples, and show how both can be understand from the multiplication principle...

From Joshua Helston

Here we provide a proof by mathematical induction for an identity in summation notation. A "note" is provided initially which helps to motivate a step that we make in the inductive step....

From Joshua Helston

Here we use a given secant ratio, draw a reference triangle, and deduce the measure of a missing angle using the 30-60-90 ratios....

From Joshua Helston

Here we do an integration by parts that required an earlier substitution to be prepared for the integration by parts....

From Joshua Helston

Here we write the gcd of two numbers as a linear combination. The screen became a little compact, so please pause the video as needed to follow the writing....

From Joshua Helston

Here we find the set of subsequential limits to a couple of sequences for practice....

From Joshua Helston

Here we find a closed form solution to a sequence that is defined recursively....

From Joshua Helston

Here we look at the concept of compactness and try to better understand it using intervals on the real number line....

From Joshua Helston