**change**. It studies infinity and how we can use it to create things.

Before we start, we need to look at what “infinity” actually is, because infinity as we know it (∞) is not actually a number, but rather an idea. To start, lets look at some notation:

\lim_{x \rightarrow \infty} f(x)

**tends towards** infinity”. It is basically looking at how the function behaves as it **approaches **infinity. Note that I put “tends towards” and “approaches” in bold, as the function can never **reach** infinity.

**if **the function behaves nicely at that point.

\lim_{x \rightarrow a} f(x) = f(a) \\ \\ \text{If $f(x)$ is continuous at $a$.}

Next up is the derivative, which basically is a way of looking at the rate of change or gradient of a function. There are many notations for a derivative, but I will be using the Lagrange notation for the most part. If f(x) is a function, f'(x) is the function’s derivative, which in itself is another function whose output for a certain value of x is the gradient of f(x) at that certain value. The formula for a derivative is as follows:

f'(x)=\lim_{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}

On our final list of notations to cover, we have the integral, which is one of the more complex ideas in introductory calculus, an integral is used when you want to find the area “under” a curve of a function (although there are many more applications than just this), the following notation for an integral is used:

\int_a^b f(x) dx \ \ \ \text{means the area under the graph from x=a to x=b}

As the intuition and formulae for integrals are far more complex, I will not be covering them in as much detail. But there are some amazing resources which I have linked at the end of this article.

\frac{d}{dx} \left( \int f(x) dx \right)=f(x)