That thing that makes your head spin like a top when you try to understand it? Yeah, that one.
To set the stage: what is calculus exactly? It’s basically math on juice. You take regular old algebra and add some fancy pants formulas, symbols, and concepts like limits, derivatives, integrals, and all sorts of other nonsense.
Let’s start with the basics: what is a limit? Well, let’s say you have a function that looks like this: f(x) = x^2 + 3x 5. Now imagine if we wanted to find out what happens when x gets really close to zero (but not actually equal to it). That’s where limits come in handy because they allow us to see how the value of a function changes as its input approaches some specific number or point.
In this case, our limit would be: lim x -> 0 f(x) = 3x 5 + x^2
Now let’s break that down step by step. First we have “lim” which stands for “limit”. Then we have the variable “x” followed by an arrow pointing to zero (->). This tells us that we want to find out what happens when x gets really close to zero but not actually equal to it.
Next, we have our function f(x) = 3x 5 + x^2. So if we plug in a value for x that’s very close to zero (but still greater than or less than zero), we can see how the output of this function changes as x gets closer and closer to zero.
For example, let’s say our input is x = 0.1. This means that x is equal to one tenth of a unit (or 1/10). When we plug in this value for x into our function f(x), we get:
f(0.1) = 3 * 0.1 5 + (0.1)^2
Simplifying that expression, we can see that the output of our function is approximately equal to -4.99 when x is very close to zero but not actually equal to it. This tells us that as x gets closer and closer to zero, the value of f(x) approaches a limit of -5 (which is what happens if you plug in x = 0 into our function).
“. It might sound confusing at first, but once you get the hang of it, calculus becomes a lot less scary and a whole lot more fun!
Now let’s move on to derivatives: what are they exactly? Well, think about it this way: if we have a function that looks like f(x) = x^2 + 3x 5, how can we find out the rate at which this function is changing as its input changes over time? That’s where derivatives come in handy because they allow us to see how fast or slow our function is moving along a given curve.
In other words: if you want to know whether your car is accelerating, decelerating, or staying the same speed on a particular road, you can use calculus to find out exactly what’s happening at any given moment in time!
“. It might sound confusing at first, but once you get the hang of it, calculus becomes a lot less scary and a whole lot more fun!