Recent content by Weightlifting

Lets just do the more 'extreme' example, I could relatively easily figure out where the vertical asymptotes of ##y=\frac{x^4-3x^3+3x-19}{x^5-9x^2+9}## would be, but how would I know which direction they would tend to for each asymptote?

For example, lets take ##y=\frac{x}{\left(x-1\right)^2}##. for ##x<-1##, the graph seems to go to negative infinity, while it't only between ##-1<x<1## that the graph goes up again. Of course this is still relatively straightforward, but the tougher the equation goes, the harder it would be for...

Hi PeroK, thanks for your input! However, my problem with this is, how close should I go, because ##y<0## for ##x<\frac{5}{2}##, but after that, it's greater than 0. How do I know how close I should go to ##x=-\frac{2}{3}##?

Sorry, first time using LaTeX, but I cannot edit my HW statement anymore it seems. It should be: Find the vertical asymptote of ##y=\frac{2x-5}{\left|3x+2\right|}##. If there is an infinite limit, what direction does it go in?

Since ##\left|3x+2\right|=0\rightarrow\ x=-\frac{2}{3}##, we know the vertical asymptote is at ##x=-\frac{2}{3}##. Looking at the limit at that point, and also looking at the left- and right-sided limit, I cannot simplify it any further...

I very much agree! At this time, it's mainly the 'challenge problems' I get stuck on, as I've got a basic understanding of the material I'm going through right now, due to my Physics BSc. However, I will have to see how I fare when I get to newer frontiers. Other than that, the following...

Thank you both! This was really helpful! I will stop looking at the solutions manual until I feel like I've solved the problem, taking both of your suggestions into account when I get stuck.

Hi all! As I've mentioned in a previous post a while ago, I've started studying Calculus from "Calculus, a complete course" by R.A. Adams & C. Essex. I've managed to get through a good part of it already, and I plan to continue to more physics related textbooks afterwards. The end-goal I have...

Thanks for your reply! I will add Special relativity, Noether's Theorem, Symmerty in modern physics, & the Feynman lectures to my to-do list! I can find basics of Special Relativity in Giancoli and the Feynman lectures will be on my to-buy list. Do you have any great recommendations for...

Hello everyone! I'm new to this forum, and I've tried looking at all the conventions on the forum, but if anything I say is out of line, please speak up! With that out of the way, I've added some of my background in physics in the spoiler, with the main questions below that. Looking back at...