In the previous post: Euler Substitution of the First Kind, we dealt with integrals involving the root of the trinomial {ax^2+bx+c}, where a>0.
But what if “a” in the trinomial is negative? Then the second kind of Euler substitution, for c>0, might help us (but not necessarily…).
When calculating square roots in Cartesian (or: algebraic) form in my Complex Numbers Course, I showed a method that involves adding a third equation to the existing system of two equations, which greatly simplifies and shortens the further calculations.
I showed this method, but didn’t justify it in any way. Recently, I received an email regarding this:
“Could you explain why we can use the method of adding a third equation when calculating the square root of a complex number?” So here’s the explanation.
This post is a kind of response to the question:
“I don’t understand something and I need an explanation, why do you simplify ‘n’? I mean that n/n is an indeterminate symbol (infinity over infinity) help because I’m already lost with this.”
Understanding what indeterminate symbols REALLY are can be quite tricky. It also raises many questions about what you “can” and “can’t” do with them.
Today, it’s going to be short. My quick question for you is:
What is the square root of x squared?
When I was still giving tutoring sessions, I asked this question to many high school and college students. Do you know how many knew the correct answer? Two.
This post is already the third in a row where I want to draw your attention to things that are worth reviewing at the very beginning of your mathematics studies at university. A quick review of them will make your life in university much easier.
Today it’s the turn of the quadratic function.
Quadratic function? The topic of the quadratic function is, of course, very broad, and I don’t mean at all that you should take a high school textbook and go through the entire chapter from cover to cover. Let’s just focus on a few important details, nuances, and traps.
Nie za wszystko musisz płacić 🙂 zarejestruj się i otrzymaj dostęp do darmowych Lekcji.
Zarejestruj się i skorzystaj z darmowych Lekcji
Recent Comments