Limits at Infinity - Basic Idea and Shortcuts!

[@JordaNoceros]

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.

[@EbonnieTaylor]

This guy has been saving my life one topic at a time

[@Mathefusions18]

I can't agree less with you.

[@rowenaravenclaw8474]

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!

[@DESTER10984]

I learn more from you in 9 minutes, than I do with my teacher in 50 minutes.

[@steveszymczak448]

that's what I'm always saying lol

[@yichizhang795]

me too!

[@freakyguyinyourmouth]

so true

[@sirlancenolasco3552]

RIght?

[@7Singularity]

You are right!

[@Mistiiiqe]

11 years later and you're still saving lives 😂 I'm glad I found this, my homework looks less scary now

[@patrickjmt]

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!!

[@yumnahossameldinibrahim3399]

Watching this from Egypt in 2020, you are really amazing in explaining calculus

[@not_ashar]

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..

[@arneljamilon308]

∞

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Im from INDIA. And i found exactly what i was looking for. You solved all my doubts. You are the best.. RIGHT CAMERA angle and all.

[@sadhanakoganti7330]

omg! like seriously i spent the past 30 mins staring at my maths book trying to figure out what they were trying to say and now i am 5 mins into your video and I understand everything. Thanks a tonn (:

[@paparazzymedia]

When a >9 minute video teaches you more than a 2hour lecture. Thanks, sir

[@thewatcherlollol]

Agree

[@Mathefusions18]

I agree with you.

[@lexinaut]

You get my UNDIVIDED attention with this concise presentation. You are an EXPONENT of clear thinking. Because of your clarity, students will tend to understand the entire presentation, rather than paying attention for just a FRACTION of the time.

[@MrSteveHatsReviews]

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

[@onedayzero]

As a math teacher, I really appreciate how well your videos are presented. Thanks! I am teaching AP Calculus AB for the first time this year and your videos are already helping me out. I have sent some links to my students and it helps them get a few minutes of review during evenings and weekends when they would normally be on Facebook or watching music videos.

[@BlondeMafia]

NOW this all makes sense. Goodness. My calculus teacher doesn't speak english and I have my first midterm tomorrow, didn't know where to turn! Really. Thank you!!!

[@darshanjoshi3242]

+patrickjmt thank you for providing free video. you made my tests easy ......you are the best maths tutor .

[@patrickjmt]

+darshan joshi thanks! :)

[@barfood8253]

Actually the same question :-( I'm a grade 12 student and I'm taking AP-calculus AB in school. We are just at the end of term2, but we have already learnt MVT and been going to optimization....that's almost the end of your list.... (and my teacher Mr. R said we are busy to get through all these calculus things since we have no time.... Can I rely on your videos to study and prepare for a university calculus 1 exam? I'm looking forward to you reply.

[@TonySoprano55]

+Live Your life absolutely yes. I just figures out something in the pcat because of Patrick

[@aliciag.1584]

Noenru I'm taking Ap-Calculus AB this year hopefully I can pass 😊

[@shussain193]

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

[@G3ToffmyJohnson]

who needs a tutor when you have Patrick? This is helping me so much in my online calc class

[@matyuktanya]

the way you explain things makes so much sense

[@patrickjmt]

thanks! :) glad it helps

[@iinteenseee]

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)!!

[@TonyAKA30]

Patrick, wish you were my calculus professor. I learn more from your 5-10 min videos than an entire 2hour lecture on the topic. Thanks!

[@tanyaradzwachinyani2326]

Sir Patric you are a life saver..l have exam next week and my lecture all he says is 'If you dont understand this simple math then see u next semester 'mxm but with you lm not gonna repeat again Um in love with your videos

[@patrickjmt]

thanks for recommending my vids to your students ( although they are probably still on facebook instead!) :) good luck teaching the class

[@pancakeofdestiny]

PatrickJMT, you're my favourite enabler of poor time-management habits ^_^ Which is to say, great video as always

[@patrickjmt]

thanks my friend!

[@Mathefusions18]

Very efficient too.

[@sarahbelski13]

You have taught me more in a few videos than my calc T.A. taught me in an entire semester. Thank you!

[@jasonly350]

my life would be so much easier if i had a calculus professor like you, Patrick !!! thank you

[@Rashedist]

-You know Pat......You made me love maths again...Thx a lot

[@Mathefusions18]

I always enjoy watching and learning from you. Great teaching.

[@patrickjmt]

I appreciate that!

[@smguesman]

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!

[@Stiner282]

so patrick you just got me through my first calc test.....i love you dude thanks so much

[@BreakneckWalrus]

I transferred into Calc AB after the class had already gone through Limits, so I've been completely devoid of this knowledge until now... Now we're learning Riemann Sums, and your other videos were *excellent* in teaching me how to do them, at least until I got to the calculation of the limit itself... ;) Then I came here, and learned it within minutes. Thank you so much!

[@DnVill]

OMG.... you just summed up hours of class into a less than 10 min video and explained it better... thank you

[@wardhively2358]

Sir, I don't know what planet you come from but you are indeed a supernatural teacher that has taught me everything I know precalculus up. Thank you thousands!

[@SarahCylon]

You're a wizard.

[@Joshemness]

thanx for the shortcuts !!! i have a math test today ! i hope the teacher gives me easy things to slove in ur shortcuts !

[@MissFutbol101]

I got an A on my math test! Watching your videos helped me a lot thank you!

[@jackpersonal9657]

wow. you are hands down the best teacher. you get straight to the point and make it as easy as possible. why cant other people do that?

[@patrickjmt]

i think it is harder to do than it would seem :)

[@jackpersonal9657]

i just watched your precise definition of a limit. That one is more tough to understand

[@Djflow824]

I've come to the conclusion that people who are left handed is generally talented at most things and or extremely good at math. Thanks Pat!

[@احمدعباس-ر9ط8ش]

I am a college student and has always been following the wonderful videos and I love your voice......

[@tgwsixers]

Finally started to get calculus thanks to your videos... just wanted to say thanks for the much needed help!

[@EssenceCoveTV]

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 :)!

[@clauditzzaaa]

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!!

[@danagamer]

you got me through algebra, then precalc, and now calculus. 1,000 Thanks!

[@TeHPHoBoS999]

Dis is beast. I was told to simply divide everything by the biggest power in the denominator, and i was like, "why?" This vid cleared it all up for me. Thank you so much.Now that I know why, i can use this wherever I want to, and twist it in odd ways and shapes. THIS IS CALCULUUUUUUUUUUUUUS!

[@clarezet1]

@patrickJMT It's so much easier to do calculus than it is to understand what calculus is doing. I did a thesis in the philosophy of maths on the consistency of different calculus systems in the 18th century, and it took a really long time to get my head around the concepts, despite having been pretty good at doing calculus computationally at school. Fair play for trying to get the idea of the thing across!

[@andreavalverde1387]

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 :)

[@jessicaimani1]

Excuse me, good sir, but can we be best friends? I was having a relatively hard time in calculus in my university, but watching your videos makes everything so simple. You've made my life one heck of a lot more logical, practical, and easier to understand. Thank you a million times for being more useful than an infinite visits to my TA's office hours and their section. Thank you so much!

[@sketch119]

Thank. You. Very. Much. I like math and all, but the way my professor teaches it is very confusing, your videos really help me understand the concept of what he attempts to say.

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First time ever in my life subscribing to a math youtube channel

[@neshnesh4674]

Thanks man,if only the world had a few more maths teachers like you!

[@zefram21]

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!

[@alo754]

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 :)

[@yafetyeshi]

i understood more than i took the lecture from class,God Bless You

[@BobbyBez77]

I don't even know why I was getting messed up in math, you made this stuff really easy. Thanks!

[@alexspoy]

I LOVE MATH...... and for me this is the must useful channel in the youtube..... god bless you patrick

[@hellolili89]

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

[@upasumith]

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

[@nehamak4332]

i can't express to you how helpful this was, thank you

[@matrixate]

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

[@nokwandamashaba5919]

I've always had a fear for maths but you always make it so easy thank you........................

[@scottmcdaniel04]

I think you are going to get me through my Calc 1 class. Thanks for the great videos they're a big help.

[@sophc193]

liked, bookmarked, saved, screenshotted. THANK YOU

[@LazarusStr]

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.

[@punjabijattchakde]

So much grateful that u help me learn week of content in only 9 minutes

[@swagcmr]

I started to study limits in my calculus course a Few days ago but i understood nothing lol Everything is clear and easy to understand with you! Thank u very much Patrick!!!!

[@XxOffTonexX]

My teacher teaches this a bit different, he has us choose the x with the greatest power in the numerator and denomonator, and get rid of the rest of the equation. Then we work on limits with only those two and get the same answers that you get with all that work.... oh but your short cuts ROCK MAN!

[@Lugo428]

I'm learning more from this guy in 5 minutes today than in the 4 hours a week I spend in math 121.

[@rocaj5559]

Midterm in two weeks! It's time to watch every single calculus video from Patrick!!!

[@patrickjmt]

you poor soul :)

[@MozyMac]

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

[@patrickjmt]

wow! that sounds just like one of the classes i teach! : ) move to austin and you can be bored in one of my classes instead!

[@ziyadali7640]

11 years old and not a single comment or like. LOL!

[@braveknight283]

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.

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Sir, you are like magic, you can teach better than 10^5 professors or doctors in math.. THNQ! PEACE OUT!

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I watch this while in my Calc Class.... My whole back row seems to always wander to PatrickJMT

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Honestly your videos have been saving me,your explanations are on point

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Thank you, thank you. You are so much more helpful than my Calculus book. Awesome tutorial

[@phlegacy]

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!

[@coolman4393]

I'm all the way at improper integrals and I forgot how to do limits. This helped so much.

[@istarzgirl]

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.

[@jaytm365]

I think that's more for horizontal asymptotes!

[@istarzgirl]

Jay Anneus Oh hey, yeah I guess I forgot to mention that x.x

[@MattDearing]

These shortcuts were not even mentioned in my course, thank you for this!

[@corbin624]

thanks for teaching me in 10 minutes what my teacher took week trying to explain

[@ixdani]

I learn more from you than I do from my professor. Thank you!

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Thank you so much! You just taught me more math in 9 min than my teacher has the entire semester!

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I'm pretty sure god sent you down from heaven to help people with math

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The Mathematical Savior!

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He is really helping much people with maths.

[@theboombody]

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.

[@samiraturk6188]

Dude my final exam is today and you just savedy life! Thank you

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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 :-)

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Bro.... THANK YOU! Simple and to the point

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I am not even able to study Calculus yet and still understand this, amazing professor

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this taught me all i needed to know for my mid-term, yay for successful cramming ! thanks @patrickJMT !!

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thanks for posting! your videos are helping sooo many people probibly all over the world and they are greatly appriciated.

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Dude you are AWESOME...me and math don't get along well but you make me like it & you just totally made me pass my calc test thanks to this video...YOU ROCK!!! (:

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Definitely broke it down perfectly with all three types. Thanks for saving my future

[@patrickjmt]

good luck!

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man you are so awesome you are gonna be the reason why I score a 5 or 4 on my ap calc test this year

[@patrickjmt]

no! i am trying to figure out how to quit my job and make a living off of providing math content! i make all these videos cause i am such a kind, geeky, loving nerd! i make $0 for this! actually, that is not true.. since i just got into utube partner program, so i will now make $10/month for all my efforts : )

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Your voice no less than X Factor, Your pen Deserves a place in the hall of fame. Thanks for the tricks Mighty Patrick 🤗 🙏🙌

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you are a gifted math teacher man!

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I appreciate what you're doing with these videos.

[@acolytes777]

This guy is a life saver!

[@Colinalb]

Makes a little sense? Makes tremendous sense! Thank you so much for the video man you've made my life that much easier!

[@andressoto67]

Im about to take a test and this helped me a ton. Thanks man 👌🏾👌🏾👍🏾

[@matrixate]

True. Given f(x)/g(x), the requirements are that they are both differentiable on an open interval (a,b) containing a "c", except possible "c" itself. This is a good method if f/g has the indeterminate form inf/inf or 0/0 at c and if Dx[g(x}] is not equal to zero for x not equaling c then you can use L'Hopital's Rule. For the most part, it will work on most of the problems encountered in a first semester calculus course, As long as everyone knows what it means for a function to differentiable.

[@one0xin]

omg thank you soo much...i have a quiz on limits tomorrow and i had no idea what it was about....but now i understand!! thx!!!