What is a Limit? Basic Idea of Limits

[devilshahul]

sir i have been watchng ur vids 4 a while.... its awesome !! :D

i would want to know whether you can help on 12thgrade cbse portions india!! please let me know.... i nhave board exams on march... worrying a lot :( dunno wat 2 do ;'(

[8Trails50]

Sometimes, I just grab a sharpie and blank paper, do my homework and talk to myself and pretend I'm PatrickJMT.

[patrickJMT]

@8Trails50 looooooooool

[hotrodfirebird]

I've watched your videos since I started taking Calculus I last spring, and because of that I managed to pull my D- to a B in the last half of the semester. I can't thank you enough, dude! I just started taking Calculus II, so hopefully your videos will continue to be of some help to me. Anyway, thanks very much!

[pennydave]

I've watched tons of your videos & I've never said thank you. So thank you for what you do! My math classes are only 50 min. and most of my teachers have bad handwriting so I pretty much learn nothing in class, but when I watch your videos, I get it the first time. I never thought I would get an A in calc 2. I got a 98% on my final (the highest score in the class). A lot of it was my determination, but sir, I give half the credit to you. Thanks :D

[patrickJMT]

@pennydave happy i could help : ) congrats on the great grade!

[nymaria2013]

OMG I love you!!!!!!!

[belittle12]

Just got my final back guess who passed with a B no less. Thanks so very much.

[patrickJMT]

@belittle12 congrats ; )

[aibee91]

Thanks for everything Patrick! I'm currently taking a somewhat higher calculus course and need to brush up on my basics!! You are Awesome!! =)

[Marcuzzorox]

Even someone who already had classes about it, it's still very informative!

[phuongduyenng]

Thank you so much! I have my math final tomorrow and all the videos you've been uploading these past few days are the topics I needed to know. ;P You're amazing!!

[MrStraffle]

Do you know anything about abstract algebra?

[Wdec29]

Thanks for everything Patrick, thanks for trig, for calc, for arithmetic, and graphing, but most of all, thanks for being you!!

[patrickJMT]

@Wdec29 : )

[Asteretsa]

Wow. Lots of top comments. :L

[SuperKmach]

Thanks pat! i have skipped many classes due to a thing called the Xbox 360, as well as the reason that the tutor isn't great, and I am usually sleep deprived at 8am! I would much rather study how I want, when I want, and I can do that with your videos! Thank You!

[LlamasWithAtaris]

Thank you, your videos saved me in AP Calc.

[GunnersOwnAll]

Hi Patrick,

I took calc already, but I want to learn everything again...is your calculus playlist in order (teaches you calculus, chronologically)?

Thanks! I've been one of your earlier fans..I started viewing your videos since I took calculus 4 years ago.

[chiguy416]

I know you get this alot, but I am currently studying Calculus I in college, and as I took precal during my high school senior year the Cal I material is quite challenging, also the fact that my professor is not to clear on his teachings doesnt help either. I would just like to let you know that your videos are dearly appreciated, thank you patrick!

[patrickJMT]

@chiguy416 you are very, very welcome ; )

[Marcuzzorox]

@chiguy416 It is very common to happen, don't forfeit!

[bharathsf]

Hey Patrick!! Which is the video which introduces integration??I am not able to find it...Thanks in advance

[PhoenixWright1000]

Why do I get the feeling that the dislikes are coming from other math teachers?

[patrickJMT]

@PhoenixWright1000 i seriously doubt that : )

[nikazar369]

@PhoenixWright1000 haha=)))))))))))))))

[thelostsole101]

wow i feel like ive learned more watching this video once than 2 weeks of my calculus class.... good stuff man!

[jojogirl2008]

THANK U! THANK U! THANK U! I appreciate u and ur videos so much!!

[redrum41987]

sounds like a porn...plug and chug

[zoecastillo717]

I love you...seriously.

[baseball101star]

How much do I have to pay you to live in my basement and help me with my homework?

[patrickJMT]

@baseball101star more than you can afford

[TheLoveformankind]

@patrickJMT LOVING UR ANSWER PATRICK

[dreadpiraterogers]

Saying a limit is "equal to" a number is not deceiving since the limit in your first example approaches 1 from both the left and right side of 5. Therefore, the limit IS 5 even if the graph is not defined at x=5.

[dreadpiraterogers]

@dreadpiraterogers I meant the limit IS 1.

[MarleyNicholeTravis]

Awesome Videos, I am really curious to know how the revenue from the apps are doing

[wolf92193]

This scares me. 2 minutes after your nice, clear video, my teacher (who was playing the video in class) made me completely confused about this subject. I have a bad feeling about this year.

[ucfkid67]

@wolf92193 wow..im in the same boat! lol

[wolf92193]

@ucfkid67 Is your teacher named Ms. Traveria?

[ucfkid67]

@wolf92193 HAHA. no.

[patrickJMT]

@wolf92193 keep watching the videos in that case! : )

[wolf92193]

@patrickJMT I will, thanks for making them :)

[1966zaim]

Hi Patric,

Wanted to thank you for a wonderful lessons.I just graduated from college with honours ,but nice thing is I am 45.I will probably continue 2 more years to get degree in Mechanical engineering.Your videos are just awesome my man.Without your help it would be a struggle ,but with your way of doing it is a just pure joy.With your help I was able to compete with young students,even with Asians.

Keep doing good job my man and God bless you.

[IndieSoul6772]

hey patrick thanks for all the help and please resolve some examples for double limits please thanks

[devianbomb]

I WILL SUCK UR DOCKS

[prantare]

Great explanation ... however lim x -> 5 (x - 4) is equal to 1... it is not deceiving in any way. Why is it?

[TheLennyXD]

@prantare Graph the line

[teppeinokanojo]

are you santa? <3

[silentsamir]

I think you are wrong when you said that the notion is deceiving because in your example when you take no. close to 5 its maximum limit is 1 not that when x stands to 5, f(x) should stands to 1 no its maximum limit i.e the maximum value of f(x) is 1. Please correct me if i am wrong. By the way amazing video and thanks a lot for the upload !!!

[ChannelTofu]

ughhh still trying to get it :|

[lost2who]

Hey Patrick can you PLEASE make a video on the epsilon-delta proof of a limit? I just really want to understand it, I looked at my book and it was hard to understand, I mean it looked weird, I sort of see where they are going but I am still very lost. I looked around and I don't think you have made a video on it, can you please make one, you explain things very well and I think you will be able to explain it.

[gur0004]

Could u finish off the good work by organizing the vids into the order that they should be view?. I mean they are scattered everywhere and it,s hard to tell which video should be seen first before moving on to the next one. Thx

[peachrocker1]

why do ppl learn about limits? why solve an equation w/ numbers close to x, why not just use x? That really confuses me because that means using indefinite quantities.

[Scarf3086]

@peachrocker1 limits are really great for proving stuff in math XD for example, they're necessary to prove continuity of a function (the fact that there are no breaks or skips where the function has no y value or "answer"). They also really help when you're dealing with x approaching infinity or infinite series. Most importantly, you need them as a backbone for derivatives! Derivatives are half of the fundamental theorem of calculus! XD I got nerdy there. Anyhow, limits are awesome!

[mateo88990]

I still cant understand what the GOAL is of these problems are you trying to get it so it doesn't equal 0, i don't understand

[jazzyenglishman]

sometimes i am almost more impressed by your handwriting than i am of the fact that your videos taught me a semesters worth of calculus in one all nighter ...

[gavinjoaquinolivas]

Idea. You should team up with Khan on Khanacademy and together the two of you (funded by Bill Gates of course) could come up with really really in-depth videos. You could focus on the math sections, freeing up time for him to make more videos. I also like your style of teaching with the paper and pen or the whiteboard and marker better than the computer screen drawings. Just a thought. Thanks for the videos Patrick!

[215vignesh]

thanks

[215vignesh]

thankx that was a great help

[teethstainedred]

i did a really good job in my first exam and it's all thanks to you. you're awesome!

[YESSENIAREIMANNuh]

Asian wives alone and try to chat her lushfmlk.info

[blueovaltrucks]

Thanks for the clear explanations. By any chance do you have video where you have a graph and you reverse engineer an equation to come up with at least 5 limits to describe the graph shown?

[stan021]

0/0 is not defined. it is NOT 0 or 1...

[z7abib77z]

Q__does 0/0= 0 or It is undefined ??

thinks very much for your explanation

you are building the humanity by your videos

in this world they should make organization thats reward people like you

If only we could express our full appreciation to you

[patrickJMT]

@z7abib77z dividing by zero is always undefined.

[Musaibaziz]

@patrickJMT what is the reason behind this?

[patrickJMT]

@Musaibaziz behind what exactly?

[chillbabe104]

@patrickJMT you're wrong.0/0 does not equal undefined. it's an exception for the rule that anything over zero is undefined. 0/0 is a special becuz zero over anything equals zero but any number over itself will always equal one. this have the characteristics of all 3 but they are all contradicting so u actually gotta do something more to the equation.

[Scarf3086]

@chillbabe104 L' Hopital's rule!

[DENlERU]

@patrickJMT: I wonder why x/0 is not defined as inf. Is it because it would be possible to break the algebra with it?

[bammy07]

@Musaibaziz it's just that dividing any number by zero is undefined.

[darknecromancer34]

@Musaibaziz supposed you have a function y=1/x, try to graph it by putting the value of x as close as to zero such as 0.5, 0.3 or 0.00001. that will help.

[jamesblackburnlynch]

@Musaibaziz 1/0 is undefined for a different reason than 0/0 so you have a good question. Basically, try this. Why is 6/2=3? Because 2*3=6. So..if 1/0=some #, then 0*some #=1. But that's impossible.

Now 0/0 is more interesting. If 0/0=some #, then 0*some #=0. But of course that is true! For what number? ALL OF THEM. For division to be a function, we can't have more than one answer to one question. So, we chose to leave 0/0 without a definition. Hence, undefined.

[Topwatch288]

@z7abib77z Well, to prove division, you could use multiplication (the inverse operation). For example, 15 divided by 3 is 5. This can be proven via 5 x 3 = 15. Now let's consider 0 / 0 = ??. Well, the multiplication version of this equation would be ?? x 0 = 0. uh-oh. ANY number could be ??. Therefore, since it's not any number in particular, 0 / 0 is undefined.

[TheMoocowmoo]

@z7abib77z Dividing is like "Putting ___ into ____ groups."

So basically, you can't put anything into 0 groups.

[Nbacks]

@z7abib77z its undefined - 0\x=0 - 0\1=there is no limit :)

[stgc1993]

dude if only i could express my full appreciation to you

[amoxaphobic]

Dude, thank you so much for this. I was soooo confused in class, but this really clears it up. I appreciate it!

[215201]

Hi, patrick

I wanted you to know that this is a good explanation of the limit, but it would benefit a lot of people if you explained the arcane "Delta epsilon" proof. AKA the formal definition of the limit, I was pissed off because it was the only question I missed on the test.

Thank You for all your help.

[neversaydie394]

according to lil wayne the sky is the limit

[DementedJuggalette]

thanks so much for these vids! im using them to help study for my college level Calc class. my teacher tends not to explain so well

[plish09krish]

THE LIMIT DOES NOT EXIST! i learned calculus from the movie mean girls

[uberethair]

Excellent :) I've got a calculus test next week this has helped a lot :D

[SuprSS787]

This is exactly the sort of explanation/demonstration I needed.

- From a second-degree seeking student from University of WI school

[patrickJMT]

@SuprSS787 perfect

[wnrsakara]

@HoldUpOneTime i totally know wachu mean!!!!

[wnrsakara]

you are AWESOME!!!! thank you a milli man!!!

[ZeGermanBoi]

Thank you so much for uploading these videos, you saved me!

[haydenrice92]

NERDS

[BlackandWhiteScarf]

@haydenrice92 NERDS UNITE!!

[20920474]

Your videos are clear, concise and far better than anything my pathetic calc teacher could muster. You are going to be the reason I get in econ 245.

[Visceral101]

PatrickJMT you have been very helpful in helping me to understand certain topics. I would like to thank you. But if i have a query about something, what I have to do to get an answer quickly, because I don't know how often you check your videos. Thanks again.

[vgadepa]

Hi

I would like to know how to get this video to be shown as youtube is blocked by my organization.I love the videos of yours to show it to benefit the kids I have .Please let me know send me an email to vgadepalli@yahoo.com

[patrickJMT]

@vgadepa if you teach school or wherever you are, contact your system administrator and let them know you want access to youtube.

i mean, it is really stupid in the first place to block youtube ... yes, now the students will be productive while in the computer lab! youtube is the ONLY interesting site to a 13 year old... (wake up old people)

[HoldUpOneTime]

@patrickJMT its funny how once I got to percalc my textbooks became useless basically. tutors are way too expensive, and I always end up using youtube and get so much more of a better understanding than my lectures where my professor goes insanely quick. used my textbook in 1st 1/2 of semester and had about a C- average, in the second half from your videos I was able to raise my grade and ended up with a B.

[garrymack]

Who ever came up with the notation on limits should be shot

[KTrap2000xl]

thanks from france

[03kingh]

Why didn't he mention L'hopitals principle?? That's makes 0/0 limits incredibly easy to deal with.

[aaacccaaa100]

Srbi uce matematiku od 1+1 do trostrukog integrala , a vi kura milivoja radite .

[BunnyHanyou]

You are the freakin bestest <3.

[gmsherry1953]

I'm merely an interested amateur, but isn't it misleading to "apologize" for the equals sign in the limit equation? Isn't the whole point of a limit that the limit really is EQUAL to the value? It's kind of like 4.99999(repeat) really EQUALING 5 -- not being arbitrarily close to 5, but actually BEING 5. I know it sounds wrong that x merely "approaches" a but the limit of f(x) actually equals the limit, but it does, right? In math, being arbitrarily close to a value is the same as equaling it?

[horseyjill28]

whaaattttt..... i suck at math. "if we put in numbers close to five" put them where? what does the limit mean, like, what are we limiting? more detail and explanation would be great.

[gmsherry1953]

@horseyjill28 In case he doesn't answer, I'll try to help. You have an equation, giving y in terms of x. y is a function of x so it's also called f(x) (f of x). You put values for x into the equation that keep getting closer to some number, like 5. You see if the values you get for y also keep getting closer to some number -- if the equation is y=x-4, they keep getting closer to 1. If the y values DO get closer to a number, then that's the limit -- in this case, the limit as x approaches 5 is 1.

[raynastee]

Hey... could you please help me. My professor is being a pain in the ass and says we can't use the "plug in chug" method. He says we have to justify it by using algebraic properties. I get the right answers and show my work, but still get marked wrong. Its awful!  ps: love your videos. You are 1million x better than my professor at a supposedly "prestigious" university.

[princemoe90]

thank you for helping me understand

[sullivanseven]

Patrick I wish you were doing videos for physics too

[blognewb]

wait... on the first part, how do you determine which numbers are "CLOSE TO 5"? How do you define that? so I can't say 6 or 4?

[patrickJMT]

@blognewb arbitrarily close

[blognewb]

@patrickJMT come on that's generic and vague. Close = non integer values? floating points only?

[patrickJMT]

@blognewb and arbitrarily close is not generic and vague. it means: i can take a number an arbitrarily small distance away

[cubencis]

@blognewb ey dont argue w patrick, hes the man. ARBITRARILY CLOSE as in, if x->5 take 4.9999 and 5.0001 and see what number they near. that term is used ALL the time when discussing limits

[blognewb]

@cubencis that's what i said, qualify arbitrary whether it pertains to a float or an integer. anyway, go ahead and continue sucking patrick's dick. he's your man all right we get it kissass. suck it

[cubencis]

@blognewb you know nothing. i can tell y no one wants to help u. homo

[blognewb]

@cubencis aw I like how you use homo in the same thread where you hail patrick as your "man". Butthurt much?

[cubencis]

@blognewb u would like it wouldnt u?? fag

[patrickJMT]

@blognewb you should look up the technical definition of a limit using epsilons and deltas. that is what you are wanting to see.

[merlinnerd1017]

@patrickJMT Hi Patrick. Yeah, I think the issue with many of us in university is trying to prove the definition of a limit...THAT screwed us over more than anything else. Could you help us out?

[MikSane]

just marry me.

[bipinformprotect]

@MikSane Sure, what's your gender? 

[teaker888]

You really know how to simplify and clearify things, such great talent. Wish all my teachers had your abilities

[neogeo328]

Could you please do a video of sgn (signum) functions?

[deceit1991]

Good video ..!

[DaHne3yoo0]

I love you....lol sounds homo but fk you're amazing! haha

[hedonism13]

1:26.

A minute and 26 seconds to acheive what all my teachers and Khan Academy couldn't do in weeks.

It was just like "OOOHHHHHH..."

[patrickJMT]

@hedonism13 : )

[mrjj970]

Dude. You are AMAZING! Who are you?? Please tell me you teach. It would be a shame if you didn't.

[patrickJMT]

@mrjj970 i am patrickjmt (as it says). i teach (on the internet if you watch my videos)

[SpacySpaceCadet]

Awesome video. I'm taking an online calculus class. Resources outside my book are a must

[ferfermas]

wow ur videos have saved my life!!! 

[PrincetonReviewable]

math is my favorite subject yet my worst grade :oo

[masonkiller666]

@PrincetonReviewable Me too :(

[Florgiethebest]

I don't speak english very well and i can understand you, isn't it great? :D ..

[fofi17studio]

f:R->R , lim( f(x) - 2f(-x) ) / x =3 when x->0

it asks to find a. limf(x) when x->0

b. limf(x)/x when x-> 0

c. lim( xf(2x) ) /x *x +f(x)*f(x) when x->0

pleaseeeeeee help me with this one .what's the solution ? i really need it .thanx in advance

[abombinreverse]

yeah, no doubt. know your trigonometric identities. absolutely right!

[bac1087]

Wow, great format, chopping it up into 5 minute intervals gives me no excuse to not squeeze one in here and there. 

[patrickJMT]

@bac1087 tryin' to keep them short and sweet. my intent is not to fully teach the material, but to provide a short resource for all the hard working students out there when they get out of class.

[emon123utube]

the fourteen(14) who dislike dis video most probably that dont like LIMIT they like Unlimit hehe

[Frankligia]

I got an A in college algebra and the highest score on the final. I couldn't have done it without your videos. I'm eternally grateful.

[patrickJMT]

@Frankligia good job! mucho congratulations

[selbeer]

you are awesome, thank you!

[usyflad]

i just wonder why there are 14 dislikes....

[patrickJMT]

@usyflad how could there not be some dislikes? : ) it is the internets!

[rafaelxsilence2]

@usyflad They probably don't like math.

[Machammerballs]

What exactly is a limit? I understand how to solve them, but it's kinda plug and chug for me. I mean what does the limit it's self represent? I kinda get that as you approach one number, you're approaching another. I guess, my question is what's the point of finding limits -

Thanks though, this video is very helpful.

[Zadamanim]

@Machammerballs its usefull for finding the slope of a curve. If you try to find the slope of a curve with a regular slope formula, you get either an "average slope" or 0/0. limit lets u see the slope just before and just after the point u want the slope of, so u can see what number the two slopes (before and after the point) are approaching. there are other uses too, like if the function is undefined at the point you are looking at you can superimpose the limit of that point, n' continuity stuf

[moneal23]

awesome vids

[dmed312]

You are an apostle for the gospel of math. Praise you sir.

[markoicu93]

Thanks so much!

I got an A on my quiz today with a VERY low class average! (It was my first perfect score in PreCalc in a while!)

[patrickJMT]

@markoicu93 my pleasure. you must dedicate your next quiz to patrickjmt!

[aahan1]

I love you man ..... :-) (Really) .....

[luckywarrior5]

wow fantastic . Thanks a lot

[amrty1]

its helps me thanx

[sexy658]

So a limit is just a prediction in math? Fuckdamn easy!

[msbabe08]

thank you!

[vancheua]

wow good video

[md2perpe]

You make really good videos, but now I feel a need to make a small comment about using the arrow:

Writing lim_{x -> a} f(x) -> c is wrong since the symbol "lim" should be seen as an operator (i.e. a type of function) mapping the following expression to a number. You can however write "f(x) -> c as x -> a".

[superc]

you just became hotter. 5/5

[Kanthir]

actually.... the "lim" is the crucial part. I don't think the arrow is needed, since the limit is a certain number. You don't get close to 5.01 and you don't get close to 4.99... It really is 5.

[tatiana30241]

My thoughts exactly. Damn right.

[KLguy133]

nice explanation but then what good is calculus when you can't find the exact gradient of a curved slope ?

Does that mean you have to repeat this process for every single point in the curve to find every single change of y over x?

mighty cumbersome no ?

[Kanthir]

Why not? Is there some problem with the video? I mean... Does the video contradict derivatives?

[jambalaiii]

thank you sir

[karlkarlkarl1234]

I am a mathematical cyborg as calculus for my cock.

[Ilir7777]

there is also the "Hopital" theoreme which helps :p

[patrickJMT]

well l'hospitals rule uses derivatives, which in turn uses limits.

so... it is completely silly to use l'hospitals rule at this point.

[Maartenn100]

Thank you very much. Finally a good explanation.

[kaungsithu1987]

oh Jesus ! really appreciation ur service . wow

[svenkatesan]

I also thought the same way as you did, when you said that ,when x tends to five the answer tends to 1 , rather than equal to one.

[cosminx2003]

thanks for that.. you explained better than my teacher

[jmadison229]

awesome video

[josher123ff]

awsome video man thanks and keep it up.