Limit at Vertical Asymptote

High school math teacher explains how to evaluate limits at a vertical asymptote!

After direct substitution of a limit, do you get a nonzero value divided by 0? If so, there is a vertical asymptote at that value of x! The answer to the limit must be infinity, negative infinity, or does not exist. Watch this video to see how to determine the answer to the limit!

Thank you for watching! Please comment below about any questions or comments you have about the problem discussed!

[jan-willemreens]

...A very good evening to you Miss Christee, I have watched your unequivocally excellent presentation breathlessly, with complete amazement and with a huge smile on my face. Maybe a little inappropriate to say to you, but in a way I'm proud of you! Sentence after sentence you spoke, took all the words out of my mouth, only to leave me speechless in the end. Highly recommended for students who are stuck in this material! However, this does mean that you are becoming a champion at slaying any math discussion between us (lol). You basically answered all my 'trick' questions I had in store for you one by one! In addition, I fully agree with you regarding your interpretation of the outcomes of the different two-sided limits. On the one hand DNE (for different directions of the one-sided limits), and on the other hand +/- INFINITY (for equal directions). But, regardless of the outcome of the two-sided limit, the information you get from the two one-sided limits remains always very important to me! Thinking of a possible function investigation. I would even suggest that the example (an orthogonal hyperbola) you use could be examined in its entirety, determining both horizontal and vertical asymptotes. Despite the fact that you redirect the viewer to a previous video. Your example lends itself well to this! Limits at infinity and infinite limits captured in one image, that completes the picture! To think I don't quite agree with the excellent textbook of the late James Stewart in this regard, who labels all types as DNE. DNE alone falsely hides a lot of valuable information, while +/- INFINITY at least still indicates which direction the graph is going on either side of the vertical asymptote! I well remember my former math teacher being very strict with this subject in particular, demanding full argumentation and certainly not just DNE! I think I share his opinion. Miss Christee, I knew right from the start that you have a great talent to produce excellent presentations, also with some humor, and this one has only strengthened my opinion! I'd love to keep watching your future video projects, AND also hope that possible math discussions will still exist (lol). Miss Christee, thank you for an excellent and enjoyable presentation, Take very good care and of course of your unforgettable Mollee, Jan-W

[camwizemusic]

Very, VERY helpful and thorough breakdown of this concept!! I always find this type of the limit to be the hardest to explain but the organization of your presentation really helped me think about this concept more intuitively. I love how you introduced a problem at the start that may be unfamiliar to viewers and would leave them wanting to know more/keep watching! Everything came full circle back to that problem at the end once the skills/foundation was built - AWESOME!! I really enjoyed your breakdown of the four graphs starting around the 1:10 mark to show how the only options for the limits are infinity or negative infinity - this tied really, really nicely into the follow-up slide where you broke down the original problem into limits from the left and right. The graph confirmation that followed was very helpful and the strong finish with the original introduction slide was brilliant! I'm glad you also took the time to distinguish/compare and contrast limits as x approaches positive or negative infinity versus limits having values of positive or negative infinity - you made this distinction very clear! Thank you for taking an abstract topic and breaking it down in a way that makes it SO much easier to understand! Looking forward to your new videos in the coming weeks! 👍