Free study guides and discussions about various topics in Mathematics. Thanks for stopping by!
You can wade into this controversy as someone who has taken Algebra 2. I would really really like you to.
Seeing multiple ways to solve a problem is one of the beautiful things about using the tools of Mathematics in creative ways. This integral, done two different ways, reveals something interesting about two inverse trig functions.
Systems of linear equations are part of high school Mathematics studies. But what about other types of systems of equations? Here, we'll look at a system that mixes exponential and logarithmic equations.
The use of trigonometric identities to rephrase problems in Calculus is a very important skill. In this limits problem, it really really helps!
Sometimes a simple change in perspective helps us solve a problem quicker. Here, a simple change in the original, somewhat daunting notation is just what we need.
Sometimes, limit problems can be difficult. This is one such limit where an advanced factoring trick unlocks the solution.
Sometimes there are multiple ways to do a problem. This one can be approached somewhat systematically, with intuition helping us out.
Sometimes a Calculus problem is about non-obvious algebra. Here is one such instance. Let’s get into it!
For Calculus students, this topic can be very tricky. Here is a discussion that can help.
Integration rules are simple. Sometimes, the rules show up in very interesting ways.
The season for difficult limits is upon us, Calculus I students! This guide is a big help! Download it!
A student brought this to a tutoring session recently. It's a really great question from the AP Calculus Exam prep materials. Nice one, College Board!
Another cool integration question from the front lines of Calc I / AP Calc.
This one is reduced to something super easy once we flex our integration muscles! King Property! Weierstrass substitution! Odd/even properties! Trig identities! One of my favorite articles to date!
Here is a link to a Desmos workbook I made that allows us to decompose any function into its odd and even components. Super useful for various integration problems in Calculus.
Papa Flammy isn’t kidding. This is an absolutely beautiful result, as is the path to getting there.
Here is a problem from a first-year DiffEq class with a straightforward solution.
Having a look at the machinations of how solving problems works sometimes results in a deeper understanding of what solving certain types of problems is all about. This differential equation problem is interesting, in that regard.
Via Popular Mechanics, this problem was more about making choices that ease solution by abstracting away some details we might not know what to do with, so as not to derail us as we work. This is my take, mostly an application of function notation.
This is a classic final exam question where it tests multiple things and asks us to jump between Math topics in order to correctly solve it. This is how we do this, Internet!