Limits at Infinity Rational, Irrational, and Trig Functions Calculus 1 AB READ DESCRIPTION

EXAMPLES Rational Functions 7:57 14:45 17:25 Irrational Functions 24:25 33:02 39:15 Trig Functions 47:01 47:40
As I lectured I misspoke a few times, at about 2:29 I should have said vertical distance, 8:20 we are looking for the highest degree of the denominator, and at 23:07 x greater than n like it was written.
In the third example at 17:25, you should divide by the largest degree in the denominator, so I should be dividing by x^3 or multiplying by 1/x^3 here. Luckily my final answer is still correct. I would have had 0/1=0. I incorrectly say in this lesson that the square root of x squared is x. The square root of x squared is the absolute value of x.

[profrobbob]

For years teaching just PreCalculus I got in the habit of dividing by x to the highest power. Getting ready to teach Calculus live for the first time I finally understood why you don't want the denominator to become zero…so the fraction is undefined. In my PreCalc class saying there is no horizontal asymptote is enough, the my Calc book you need to be able to say if the function approaches infinity or -infinity as x approaches + - infinity.

[profrobbob]

That is something I want to do. I will be learning as I go...just like I am doing with Youtube. I hope you have found on the homepage of my channel I do have the videos organized:):):) I have playlists for Geometry, Algebra2, Trigonometry, PreCalculus, AP Statistics, and now working on Calculus...along with a few more playlists. Thank you for watching and all of your support, I appreciate it very much...and so does my wife! I am excited you like my teaching style so much:D

[profrobbob]

I have another video where I do two more examples of Horizontal Asymptotes of Irrational Functions. It is a PreCalculus video but Finding Vertical Asymptotes and Holes of Rational Equations may help with the hole definition. If a factor in the denominator can = 0 but cancel with a factor in the numerator the graph has a hole at that domain value where the factor that could be cancelled = 0. If the factor that can = 0 in the den. cannot cancel you will probably have a vertical asymptote.

[CaseyKC]

Thank you so much. im taking a whole calc class in like a month and a half and it is going extremly fast. you help so much. and i would of failed trig if it wasn't for your trig videos. thanks man. much appreciated

[profrobbob]

And THANK YOU for watching and learning from my channel:)...and please share your story and my channel with your friends from class too!

[profrobbob]

Thank you Erick!...and thanks for supporting by liking and subscribing! Please help my channel groW by telling your friends to do the same:)

[profrobbob]

As x approaches Infiniti the cosine function will continue it same smooth pattern of oscillating between -1 and 1. Since the function never settles to approach a constant value, there is no solution or limit.

[profrobbob]

You're welcome...and THANKS for being a loyal, supportive subscriber. I really appreciate the channel dedication! And thanks for taking the time to comment and share your story...I hope you also share my channel with your classmates:D (Sorry for the delayed reply...I have the approval set on all comments:)

[ryankim]

You are really helpful! Im really struggling in AP Calc AB but you really helped me to finish my hw! thank you! like literally.. each problem took me like less than 10 sec to solve. really like how you teach :D

[profrobbob]

Sinx never settles to approach a constant y value as x->infinity so there is no limit.

[mvpvic]

Thank You so much!!!! This video was very helpful. Thank you for being kind enough to upload it

[catma]

the most difficult part about learning calculus “on my own” is using what I learned from here and applying it to what my teacher wants me to do. you break down the information so well, but I still struggle doing my homework

[sandlertossone]

I am slightly confused on the irrational functions. On 31:40 you multiplied the denominator by a negative value but not the numerator. You did it on the rational functions so is there a reason you would only do it for just the denominator? Thanks again. My college professor just does problems from the book and doesn't relate concepts so you can use how problems are derived and not try to memorize them. The first test I got a 96, thanks to your explaining epsilon delta, and the last one I got a 105%. This is all you and your help. Even though I am going for engineering, I really wish I would have started 20 years ago and become a teacher. A few of my classmates are now watching your videos since I gave them the channel last month. For them and myself, Thanks again.

[justinemendiola]

watching this the day of my test and everything is clear now. THANK YOU!!!!

[profrobbob]

My Algebra 2 & Pre Calculus playlists are complete...if that is the question.

[slayerjj]

The way i learned it is to factor out a largest x degree from the denominator, and the same x degree is factored out in the numerator. ends up doing the same thing but i believe its a bit easier then multiplying 1/x^(to the what ever) to each number.

[sandlertossone]

Nevermind the sinx/x. I understand the answer. You did really great on the epsilon delta and was wondering if you could find time to do a video on some using N and M for the infinite limits since there are a lot of questions in the book about them?

[RoodyRoo]

10:59 lol I do the same thing. If the mark doesn't look neat enough I have to go back and clean it up. Thanks for the video!

[mayraolvera]

awesome video! Would this explanation also apply to the lim as x approaches infinity of sin x?

[EmmalieMorisseau]

calc exam in a few. Thank you for this video. Very helpful!!!!