Limits at Infinity - Basic Idea and Shortcuts!
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- Опубликовано: 28 сен 2024
- Limits at Infinity with Rational Functions - In this video, we explore how to compute limits as
𝑥
x approaches either positive or negative infinity, specifically focusing on rational functions. You'll learn key shortcuts and techniques that are applicable to these types of functions, helping you tackle these types of limit problems efficiently. Mastering these concepts will provide a significant advantage when solving similar limits in algebra, calculus, and beyond.
What You Will Learn:
How to compute limits as 𝑥 → ∞ and 𝑥 →−∞ for rational functions.
Shortcuts and strategies for dealing with rational functions in limit problems.
Understanding the behavior of rational functions at extreme values.
Practical examples that will reinforce key limit concepts and techniques.
Support my work on Patreon: www.patreon.co...
#Calculus #Limits #Infinity #RationalFunctions #LimitAtInfinity #CalculusHelp #MathTips #MathShortcuts #AsymptoticBehavior #Mathematics #MathTutorial #RationalLimits #MathTricks #Algebra #LearningMath
At the end he says “Hope this makes a little sense”.....dude, you just solved all my problems! How is it that you can literally answer all my questions in 9min when my teacher can’t even make sense to me in 2hrs? YOU ARE AWESOME!
patrick, ive watched you all 4 college years, and thanks to you im graduating as an electrical engineer. i hope youre off somewhere happy making a family and good money, youre one of the few men in this day and age that deserves it all. Thanks buddy, couldnt have got my bachelors without you.
This guy has been saving my life one topic at a time
I can't agree less with you.
11 years later and you're still saving lives 😂 I'm glad I found this, my homework looks less scary now
well, just be happy you live in the internet age : )
and having crappy teachers is a part of school, along with the amazing ones! sorry you currently have one of the bad ones though : )
i am your teacher now!!
Watching this from Egypt in 2020, you are really amazing in explaining calculus
I know I am posting a comment after 11 years of upload of the video but I have watched it now. All of your videos are really helpful but I have a question reply it if you see this comment
In your Example, in denominator where 7/x^3 shouldn't it be negative infinity when we put negative infinity because power is 3 and negative of a power is negative..
∞
When a >9 minute video teaches you more than a 2hour lecture. Thanks, sir
Agree
I agree with you.
PatrickJMT, you're my favourite enabler of poor time-management habits ^_^ Which is to say, great video as always
thanks my friend!
Very efficient too.
thanks for recommending my vids to your students ( although they are probably still on facebook instead!) :) good luck teaching the class
Oh wow, MyMathlab should REALLY hire you for their video portion. Seriously, those people are so dead when they try to explain anything, and when they do they only do one example, usually, which is never enough.
You are the best :)
EXTREMELY helpful. My calc teacher said "if u dont know anythign about calc , dont worry," but as soon as he was done explaining where he was from and blah blah he just went straight into Limits and i was COMPLETELY lost. I would pay you for help!!!!! Great video.
-Steve
You got me through pre-calculus, seriously, and now you're getting me through Applied Calculus, seriously. You seem to do the exact type of problems I need help with. patrickjmt FOR PRESIDENT
who needs a tutor when you have Patrick? This is helping me so much in my online calc class
I got an A on my math test! Watching your videos helped me a lot thank you!
You are the BEST teacher ever!! I'm going to be sure to share your tips and shortcuts with my classmates!! My professor sorry to day this but he sucks!! I will continue to use your videos!! THANK YOU SOO MUCH!! This class has been stressing me out to the point of tears, you have no idea!
FINALLY I understood something about those limits with infinity! Thank you! I have an exam at Calculus next week and I really need to remember so many things, thank you for this video!!
First time ever in my life subscribing to a math youtube channel
this class was practically bringing tears to my eyes cause i couldn't understand anything, i'm not kidding. you freaking saved my life. thank you SO SO SO much, i understand everything so much more now (and the tips at the end were awesome)!!
OMG THANK YOU SO MUCH. I have a precalc test tomorrow and this is the only thing I did not get until your helpful video :)
These shortcuts were not even mentioned in my course, thank you for this!
so patrick you just got me through my first calc test.....i love you dude thanks so much
You're a wizard.
@Remindor great, that is exactly how i want it to feel
-You know Pat......You made me love maths again...Thx a lot
@danagamer you are very welcome!
That trick at the end is great. I actually mentioned it in class the other day because I remembered those rules from algebra. My teacher still won't let me skip the steps because she wants to see me "do calculus work." It's still a nice way to check my answer though.
Good job. You can also take the derivative of the numerator and the denominator independently to form a new fraction, then keep doing that until it looks easy enough to intuit the limit. That's another way. It's a more advanced method of Calculus but it's a good way to check your answers. It's called L'Hopital's Rule. Here's an example:
lim (x^2/x^3)
x->inf
Dx[x^2]/Dx[x^3]=2x/3x^2
then do it again to the result
Dx[2x]/Dx[3x^2]=2/3x
and again
Dx[2]/Dx[3x]=0/3
Hence
lim(x^2/x^3)=0
x->inf
Thank you soooooooooo much we have to complete a presentation on problems like this in my class this clears it up so much thank you God bless your brain :-)
@oakkathebest in general, you have to check both. however, for rational functions, the value is always the same which is why i do not check both positive and negative infinity
Sir, you are like magic, you can teach better than 10^5 professors or doctors in math..
THNQ!
PEACE OUT!
Thank you very much. Reading the text from the book doesn't always help me. Honestly, as I watch this video for the first time, I understand it a little, but it is better than what the professor or textbook has explained. I will watch repeatedly to make it my first language. You really have helped though. I send you an extreme thank you from NYC.
Seriously, you make it so clear! I'm a terrible procrastinator when it comes to studying things I don't like, but when I watch your videos it begins to grow on me and I end up feeling like doing some exercises (boy does that sound weird to me :P). Simply put, you're THE man! Please keep making more videos, they're greatly appreciated!
i think in usa, probably either Calculus - By Stewart or a Calculus book by Larson are very very often used in college. can get a very cheap one off of ebay... just get a slightly older edition. but people have their gripes about these books too, but i like them overall.
Dear Mr. Patrick,
You are a wonderful teacher. I like your teaching methods very much. It is very clear description.
Thank you very much
Sumith from Sri Lanka
Your voice no less than X Factor, Your pen Deserves a place in the hall of fame. Thanks for the tricks Mighty Patrick 🤗 🙏🙌
you are my hero, i have math mid-term tomorrow and I had no idea what limits are, i wish i knew your channel before :D
Thank you for posting this and actually explaining the content!!! I have no idea what I'm doing in my calc class (since the 2nd day of class and I took a 0 on a 3 question quiz because I had no idea what to do). I have another quiz today and I can't wait to take it now!!! Thanks again!
Thank you so much! I've been dealing with limits for so many years now and I have never really understood any of them. But watching just the first half of this video helped me so much. Your way is so much simpler to remember. Thanks again :)!
you got me through algebra, then precalc, and now calculus. 1,000 Thanks!
i understood more than i took the lecture from class,God Bless You
Man, it has been a long time since I've done these limit problems. I've mostly been investigating the mathematician Georg Cantor's weird math work on my own for the past few years. I made some crazy videos on youtube inspired by his methods. One is called "Does Counting Exist?" and the other is called "Can Something Be Twice As Big As Itself?" At some point math just explodes on itself. I'd say never take it too seriously.
Midterm in two weeks! It's time to watch every single calculus video from Patrick!!!
you poor soul :)
So much grateful that u help me learn week of content in only 9 minutes
From my teacher to help remember: BOBO-bigger on bottom is zero,BOTU-bigger on top is undefined (I know that you say either +/- infinity so I'm sorry if BOTU is wrong),and BETC bottom equals top is the coefficient.
I think that's more for horizontal asymptotes!
Jay Anneus Oh hey, yeah I guess I forgot to mention that x.x
this taught me all i needed to know for my mid-term, yay for successful cramming ! thanks @patrickJMT !!
Thank you, thank you. You are so much more helpful than my Calculus book. Awesome tutorial
I'm all the way at improper integrals and I forgot how to do limits. This helped so much.
Thanks man,if only the world had a few more maths teachers like you!
Thank you so much! I really needed help on this topic because I'm doing my homework and I couldn't find any examples in my textbook involving negative infinity. I actually UNDERSTOOD it :D
thanks for teaching me in 10 minutes what my teacher took week trying to explain
thanks! thanks for pointing out some additional techniques that may help others out too!
ps - I have tons of videos about L'Hospitals rule on my website!! : )
Im about to take a test and this helped me a ton. Thanks man 👌🏾👌🏾👍🏾
Your vids are slow enough for me to understand and fast enoguh to keep up with my classes in school and have plenty of free time : D perfect!
Thank you sensei
@isuredolovemusic thank ya very much
I am not even able to study Calculus yet and still understand this, amazing professor
@MustangRacer13 i am gonna pwn online math stuff before it is all over!
before I watch this video I was planing to drop the subject ....but
you're a the MathMan ... 4real ..
Your tutorials are so great! Really helping me understand (and actually enjoy!) mathematics! Thanks so much!
This guy is a life saver!
OMG....you just explained everything my teacher said but better..thank you so much...
My book that I'm "supposed" to learn from doesn't even show me this process, it just shows the question and answer and pisses me off. Thankyou you are a lot of help
you are a gifted math teacher man!
@elevatorbuttons you are very welcome :)
thanks bro this helps me for our exam tomorrow :D i'm still struggling a bit in limits of a function because i forgotten how to factor but still know some :D i'm grade 10
dude ure amazing bro ..you saved my life ...i felt like i was gonna fail my next calculus exam cause i only took pre-calc in high school ..now my chinese gf won't think im a dumbass anymore ;)
YOU SIR ARE A MATH GOD. WORDS CANNOT EVEN EXPRESS YOUR ALL MIGHTYNESS!! THANK YOU SO MUCH!!! :D
@Dangcosmo
@Dangcosmo it is amazing how many people who have a favorite hobby listed as: 'gaming' let me know how nerdy i am. i am not sure you realize it, but 'gaming' is the #1 sign of a super geek (which is fine by me). just a little: fyi
liked, bookmarked, saved, screenshotted.
THANK YOU
I learn more from you than I do from my professor. Thank you!
can you make a few vids on everything u need to know about lines angles and how to solve tricky angle problems?
Uhhhh, no! I'm not on FB and I study hard. Some teachers really suck at teaching. And I'm no dummy. You just make it easy, so accept the compliment and keep the videos coming! ( :
I am a student of class 7 and I am learning Calculus! It is the most amazing subject one has ever studied. My name is Indresh Mukherjee and this icon is my father's.
I get it!! So you basically want to find the horizontal asymptote because the limit of the graph will be heading toward the asymptote...Right?
Thanks man! Big help. My prelim. exam is tomorrow. I hope I can pass.
@Zenstrummer yes but if you think about it the concept of this limit thing is just seeing what happens around large or tiny numbers and you are just plugging them in for x. just like anyone can use a calculator, anyone can plug in the numbers in their heads as well, but why waste time doing it if you are just gonna check your answer anyway with a calculator?! you should check too btw
You're the man Patrick! Much respect
@That1Smile no
omg awesome work. You probably won't care, but you just saved my life.
hopefully more's to come!!
Thank you, you just saved my midterm mark!
I swear to god this really helps me. Thanks Patrick !
thank you so much, it makes me wonder if my lecturer is really bad, or if I have some attention span issues in lectures.
From UK, thank you so much
@vivt ha, glad you do not find me too annoying to listen to, like some : )
I think you're wrong at 4:00, you should divide each term by x^4, not x^3 because the highest degree there is x^4.
Please correct me if I'm wrong, I'll appreciate it.
@charlieucc good luck : )
You are my new favourite person! Thank you soooo much for your videos! :)
u r amazing teacher one request post more difficult and different type questions..
patric in second question you said take the highest power of x
why did you not take the highest power of denominator which is x to the power of 4 ?
thanks that is a lot more clearer than how my teacher taught it.
@mypinkdollprincess well, i think there are more guys doing math/science than females, so that is part of it.
plus people totally make up garbage accounts on youtube, so i would not trust the stats all that much!
i have already
You're the best man , u made it easier.
thanks for the video, it really helped me understand limits at infinity
@prasiprassi : )
why did you not take the sign of 7/x^3 into account? would that not make it a negative divided by a negative so the limits a positive
YOU ARE AWESOME! I'm gonna pass calc1 thanks to you!
This helps alot! so much better then my teacher too
Thank u soo much ...u r bestest teacher ever.
you sound like the students in my classes! : )
You sir are a hero! Thank you!