Today, I'll explain how to calculate another limit that is somewhat different than the one here. Specifically, I'll explain how to calculate this: \begin{equation} \begin{split} \lim_{x \to 6} \frac{x \;…

Today, I'll explain how to calculate a limit that is somewhat different than the one here. Specifically, I'll explain how to calculate this: \begin{equation} \begin{split} \lim_{x \to 3} \frac{x^2 \;…

Today, I'll explain how to calculate the following limit: \begin{equation} \begin{split} \lim_{x \to 5} \frac{x^2 \; - \, 25}{x \; - \, 5} = 10 \end{split} \end{equation} Notice that both…

In a previous blog, I described how the half life of a particle can be used to solve exponential decay problems. In this blog, I will use logarithms to describe…

Sometimes, there are tricky questions such as the following: $$ \lim_{x \to 3} \frac{x \; - \, 3}{\sqrt{x^2 \; - \, 9}} $$ Both the numerator and the denominator tend…

How do you calculate the sum of an infinite number of things? Normally, that is impossible. However, if the infinite sum is a geometric series, it can be done. First,…

In calculus, people are interested in calculating limits such as the following: $$ \lim_{x \to \infty} \frac{3x^3 + 5}{2x^3 \; - \; 1,000,000\,x^2} $$ To calculate this, we need to…

The half-life of a substance is the amount of time it takes for that substance to deplete by 50 percent. A typical problem goes as follows: The half-life of uranium…

The exponential function is frequently used in Calculus. I'll explain what this function is like in this post. Recall that you can write powers of two like this (we use…

Want to understand parabolas without having to read a textbook? This post demystifies parabolas by describing their most important features. Knowing these points will make any discussion on these graphs…