Have you seen my latest blunder? Here it is:

To magnify my shame, here is the video version:

Limit with factorial leads to familiar solution (YouTube).

The goal was to solve this limit:

If you have yet to see the new Netflix mini-series, *The Queen’s Gambit*, worry not. This article contains (almost) no spoilers.

YouTube math aficionado, Dr. Peyam has published a video featuring this limit:

I received an email the other day — a response to the antiderivative challenge. Enjoy it. And ask yourself: what does maths do for *you*?

What is it that drives folks … to delight in taking five lines to solve a maths question that we could solve in one line?

Then read further.

Is it possible to solve ∫(1/t)dt using the reverse power law?

We can write the problem as follows:

The Power Rule for derivatives is one of the first tricks we learn in Calculus I. It’s such a refreshing alternative to using the limit definition.

Let’s start with a question. For the graph of* xⁿ*, what is the slope at a given point?

For example, *f(x) =x². *We can represent *f(x)* as the area of a square with sides, *x*. We increase each side by an infinitesimal, d*x*.

Yesterday (October 30, 2020), YouTuber Steven Chow (blackpenredpen) posted a video with this goal: Integrate x² without the power rule. Before seeing Steve’s solution, I posted my own video. (I didn’t want to be unduly influenced.)

Have a crack at it yourself. Then see how I solved it (below).

You want to find the roots of a quadratic polynomial. Good news! The method of *completing the square* always works. What makes that so, and what other information can we glean from this method?

Let’s find out with an example. We’ll find the roots of:

The best way to define the Squeeze Theorem is with an example. We’ll use it to prove the following identity:

How do we take the derivative of a product of functions? You may have memorized this formula:

This derivation of the power rule does not use limits. Its inspiration is Abraham Robinson’s non-standard analysis and hyper-real numbers.

If you learned a derivation of the power rule, it probably started something with a definition of the derivative:

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