High Schoolcalculus

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Calculus can be tough stuff. Calc AB was the first AP class I ever took in high school, and though I love the subject now, I certainly didn’t love it when I was first struggling with limits or with the chain rule for derivatives.

Taylor series can often seem a bit mysterious the first time that we learn about them. The formula for the Taylor series of a function f(x) around a point x=a is given by

One topic that seemed a bit mysterious and magic to me when I first learned calculus was implicit differentiation. In this post, we’ll start by reviewing some examples of implicit differentiation and then discuss why implicit differentiation works.

The symbol “dx” comes up everywhere in calculus. For example:

Suppose that we have many towns spread across the country and we are trying to connect them with a network of roads. If we would like to do so by laying as little road as possible, how do we do it? In this blog post, we will use Calculus to tackle a special case of this optimization problem.

Have you ever wondered where the formulas for volumes that you studied way back in geometry come from?

If polar equations have you second-guessing your future as a nuclear physicist, fret not! Almost every pre-calculus student I have tutored has struggled here, and it isn’t surprising at all. Remember the first time you saw an equation and were introduced to these strange x and y variables? It may seem like second nature now, but you were ...