In this post, I want to have a look at a really neat part of calculus, Taylor series. It’s essentially a process you can use to approximate some graph, e.g. e^{x}, using a polynomial – the idea is, the higher order the polynomial, the more accurate the approximation gets.

## Let’s dive in! (This gets a bit tricky)

How does it work? First, some terminology – the first order approximation is a linear approximation (so ax+b), second order is quadratic (ax^{2} + bx + c), and so on. So let’s start with a first order approximation of, say, e^{x}.

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