Remember, when I said I was refreshing on my Pre-calculus? I was expecting it to be a quick refresher, but it turns out that there are many concepts from pre-calculus that I never learned properly the first time. As I go through and relearn these pre-calculus skills, I realise that they are the exact same skills that screwed me over in my first calculus classes.
- Simplifying Radical Forms
Sounds so easy, until you get something like this,
and you have to figure out how to turn this into its simplest form. Just so you know, the correct answer is
- Algebraic Symbol Manipulation
This one got me twice. The first time, and then the second time when I was reviewing it two days later, to see if I still knew how to do it.
I had to play around with the variables for half an hour before I realised you just have to get the x’s on the same side, and then factor the x out.
- Solving Equations in Radical Form
This one is a skill you need to succeed with integrals. Most equations in radical form are easy. It’s when you throw in weird shit like fractional exponents that you have to really think “out of the box”.
The trick here is to turn the equation into a classical quadratic equation,
then make a substitution.
Now you can solve the equation like normal.
u now is equal to either -3 or 1. Substitute y^(1/3) back in… and you have.