Small typo

[trianta2]

Currently:

That is, it cany be any expression

Change to:

That is, it can be any expression

mlvu.github.io/preliminaries/index.md

Line 984 in 1837eec

<p >To work out the following examples, we'll need to know how to think about <em>limits</em>. In a proper calculus course, we'd take you through both the intuition behind them and then derive the rules for correctly working out algebraic derivations with them. <br></p><aside >These <a href="https://en.wikipedia.org/wiki/Limit_of_a_function#Properties"><strong class="blue">aren't complex</strong></a>, so if you've never seen them, it's worth having a look.<br></aside><p >However, once we've used limits to derive the rules for differentiation, we won't see them again in the rest of the course, so we can allow ourselves a little shortcut. There are only three things we need to understand about how limits work.<br></p><p >First, the function for which we take the limit, g(x) here, can be rewritten using any of the rules of algebra. This just turns it into the same function, expressed differently, so it doesn't change the limit we're expressing with the notation "lim g(x)".<br></p><p >If the function to the right of the "lim" is a sum of two other functions, like x<sup>2</sup> + x is a sum of the functions x<sup>2</sup> and x, then the limit of that sum is just the limit of the first term by itself plus the limit of the second term by itself.<br></p><p >If our limit is for <span>h</span> going to zero, and the function to the right of "lim" is just <span>h</span> by itself, then the result is just 0. This hopefully makes intuitive sense: if we make h smaller and smaller so that it converges to zero, then the function "<span>h</span>" becomes zero.<br></p><p >If the function <span class="blue">c</span> to the right of "lim" is constant with respect to h. That is, it cany be any expression, with any number of variables, but it doesn't contain <span>h</span>, then the result is just <span class="blue">c</span>. Again, this should make intuitive sense. If we make <span>h</span> smaller and smaller, but its value doesn't affect <span class="blue">c</span>, then the result will just be <span class="blue">c</span>.<br></p><p >To properly work out all limits you might encounter, you'll need a little more than this (not much though), but to illustrate the principle we can make do with these four rules.<br></p><p ></p>