Free study guides and discussions about various topics in Mathematics. Thanks for stopping by!
Implicit differentiation is very useful in a number of tricky situations. Here, we'll use implicit differentiation twice to solve a tough problem, noting some important choices we make along the way.
You were great at solving absolute value equations at one time, but now that you're working with absolute value inequalities, you can't get the right answer. Make the change!
Applications of trigonometric identities are sup er useful in this triangle area problem.
Using a little insight, we can make a problem that looks to have difficult calculations a little easier.
It took me several tries to get the differentiation correct! This is a tough one that demonstrates how keeping organized - somehow - can be an important part of problem solving.
A great example of how using a little bit of a trick avoids a whole lot of work. Nimble algebra is where it's at!
Let’s tie everything together and check out all the rules in action as we make sense of our gibberish problem!
Calculating roots is up next. Simplest radical form, n-th roots, prime factors. Next steps!
The gibberish question: simplifying some morass of exponents, roots, rational expressions, etc. Lots to manage; all can be dealt with using simple rules. Dig in.
A recent student of mine pointed out the ellipse-hyperbola connection and made it way more specific than a previous connection I noticed.
One of the coolest tricks I’ve seen. Seriously.
Sometimes we need some combination of multiple integration techniques to solve an integration problem. Here is one such case, featuring a rational function.
A really cool factoring application and a really cool FOIL trick. Faster calculations! No letters! No variables!
A classic problem about framing a photograph.
Systems of equations are not always linear, as we see in early Algebra classes. The techniques are mostly the same for other kinds of systems.
This problem is all about how the definitions of basic geometric figures often imply many things to help us solve problems!
Anything that is intrinsically periodic can be described by trigonometric functions. Here is an interesting one. And no, the Earth isn’t flat. Read on.
This one took some work and some insight. The detours were fun and interesting. Read all about it!
An interesting one to flex our muscles on some limit rules and limit calculations.