Continuity - Part 1 of 2

[lovenaturedogs16]

@patrickJMT, Thank you so much! I have an AP Calculus midterm tomorrow and your very clear explanations are so helpful.

[mcrockafelladragon]

if i have to watch one more ad i dont know what ill do

[whachalookingfor]

@mcrockafelladragon you will watch another one. if there's an ad it normally means the person in charge of the account is allowing for ads thus they get some money from it. "so it isn't that bad really. and besides you can skip more than half of the ads. so quit complaining please.

[mcrockafelladragon]

@whachalookingfor You should learn how to use commas.

[cuteannabanana]

I love you dude! =)))

[rohailwasim]

dude . you are epic :D

[progressive09]

patrickJMT is the BEST MATH TEACHER. Everytime I can't understand the lesson of my professor I refer to his videos.

[bulatgibadullin]

Got a test tomorrow on Limits + Continuity. Sitting here at 2am trying to find some helpful videos on youtube. You sir are the man!

[patrickJMT]

@bulatgibadullin good luck! there is a calculus 1 playlist on my channel page - stuff may be a bit more organized if you need it

[KarateKid430]

@bulatgibadullin Literally tomorrow? I ask if your brain hasn't shrivelled up from a lack of sleep and since it was 2am, it is actually 'today'. No offence.

[1234550stars54321]

First off dude your the man you help when so much when my teacher fails keep making more videos. ALSO LIKE IF YOU WERE IMPRESSED AT 5: 35 WHEN HE ERASED THE SMUDGE WITHOUT ERASING PART OF THE GRAPH'S AXISES.

[lmafo4utube]

OHHhh your using the same whiteboard as me so much win. Watching every single one of your videos.....makes so much sense.

[ICOD73]

hhh Try 2x speed ... First video to try this new feature on

[DMANGUY14]

I would go gay for you. Thats how great this videos are

[neenie87]

I HATE LIMITS!!!

I HAVE A TEST TOMORROW ON THIS STUFF AND IM FREAKING OUT.

I HATE MY LIFE

alright i'm done venting

[patrickJMT]

@neenie87 it is not the end of the world, i promise. it is only a test : )

[zoecastillo717]

Can you do more examples of Continuity problems please?

[aw741]

thank you soooo much!!!

[bestfriends1901]

These things made me cry while trying to review for my test tomorrow! Thank you soooo much for making these videos! I appreciate it! :D More power to you!

[zoecastillo717]

Haha I just realized you're left handed too!

[dreamtiger347]

hey omg your videos are great! Thanks alot. but do you have videos that explain continuity and limits with piecewise functions. But the functions dont have inequalities instead they have equal signs. There so confusing. For example f(X) 3X^2 +5 and x cant equal 1 and then 6 and X equals 1. I dont understand how to write a continous extension or if there removable. Thanks so much for your time

[Haydrothedragon]

Damn continuity.DAMNIT TO HELL!! lol

[sweetjaminz]

Thank you for making this! I have a quiz tomorrow in Calculus and I'm staying up late studying/watching the videos you made! :)

[trickpaulmino]

I dropped out of my Calcu class. I'm taking yours instead. hahaha

[Vanchee09]

No I will not make out with you~!

[mpatt79]

If you can't wrap your head around these mathematical concepts, don't take it out on Patrick and hit "dislike", blame your rents for not giving you a brain.

[omogaju]

you are a god!!!

[JohnRater]

you fucking own man, I see that Verizon is advertising on your page, I'm definitely thinking about switching to their service because it's better and because if they support you, I'll support them! thanks dawg

[patrickJMT]

@JohnRater ha well, i think it is just random ads on my video

[neversaydie394]

he puts his pants on in the morning like everyone else....but first he explains calculus. -jp great vid man thanks

[arielalexis2010]

Marry me?

[haahoohee93]

Oh, nice, thank you so much

[Kingboy676]

شكراً جزيلا

thank you

[xcstacy2]

is the "jump" the same as essential discontinuity? just phrased differently?

[austifications]

More like... ContiNUDITY! hahaha. just kidding let freedom reign.

[patrickJMT]

@austifications ha, good comment : )

[Zolika4]

@austifications penis!

[sankamuru]

Your videos helps me a lot. Thank You so much!!!

[XtRedChaos]

YEA!! TEXAS RULES!!!

[tardfarms]

thanks for the concise explanation in plain english this was helpful. but please put some pants on.

[patrickJMT]

@tardfarms never

[mikeygdawg]

@princetonjet rofl you're kidding right?

[gikiian]

lol, he's naked!! pause at 3:16

[patrickJMT]

@gikiian ha, or just wearing shorts in the oppressive texas heat : )

[gikiian]

@patrickJMT Hehe, but really this video was awesome :), really helped :) do them naked if you really feel easy. We love you :D

[patrickJMT]

@gikiian thanks! cause sometimes... i do!

[r0xyfoxxy5]

thank you so much

I'm in class just looking at the board and feeling dumb

and now I kind of get it thank you mucho

[EdMahoney19]

I got an A in Precalculus I and II using these videos and I got an A in Calculus I, using them. Check them out. They're great previews for chapters.

[kupop0w]

what about limits other than the ones named? arent those called discontinuities of the second kind? thats what my book says i think.

[13eanerMan]

Thanks for the video. Reviewing for my final exam. Your videos are really helping.

[patrickJMT]

@princetonjet in lieu of that, the best thing to do is to buy a roll of foil wrap, and make a big metallic helmet and wear it during your exam.

i am gonna get into a zen pose in the morning and project mathematical insights into the cosmos. the bigger your foil helmet, the more of them you will receive. you may also get some funny looks, but you can just laugh at them, cause YOU are the one who knows whats really up

[itsandrewbiotch]

patrick!

where can i send donations through paypal?

[xK3rune]

@itsandrewbiotch Click on his site on the info then click on Donations on the left.

[TheMightyAlgernon]

You're doing a great work

[andreasbalzer1988]

@patrickJMT: Do you have a video about continuity proven with eplison/delta-approach? e.g for |x| or x^2

[elhermosouno]

if, in the last example, the right side of the graph did head towards negative infinity as x -> a, would that then be jump discontinuity or infinite discontinuity?

[10243406]

Nice work. I can learn this on my own, but watching someone teach it solidifies it further. thanks ======D~~~~~

[lilmsunshine1]

i suck in calc!! i literally day dream while the prof is teaching,,,,mathematics is not my piece of cake. :(

[aad1236]

this is like the whole lecture my teacher gave nice

[xecut10n3r]

@Sectorsophia

ahah you shouldve put a smiley face at the end of that last sentence!

[meterotronic]

Without advanced math we would lack the explanation of the universe around us, Physics for example could not live without Calculus...You never fully understand math...you just get used to doing the same things over...if it were easy we would all be math majors..=)

[makeupandshoes]

thank you SO much for this.

[nilloc93]

i agree with Teganor what the fuck is the point of advanced math? all i need it for is a damn computer programming degree. wtf do i need advanced math for? i need to know physics and scripts, not this shit

[Sectorsophia]

@nilloc93 For those who are content with mankind forever existing in the stone age, higher math is, as you say, shit. And when you're a 17 year old smartass, it's easy to miss the point of higher math.

And luckily for you, here on planet earth, your propensity toward idiocy is not uncommon.  You'll fit in nicely amongst the masses! Now, go put on your uniform and get ready for tedious unfulfilling labor for the rest of your pathetic existence.

[sponsoredwalk1]

Haha, nicely done old chap ;)

Plus, I wouldn't really call continuity, when applied to basic calculus, advanced math compared to some of the scary things I've seen :p

[rgrybra]

Thank you!

[alytrombley]

THANK YOU!!!!

You make it so much clearer than my prof does.

Your videos are life savers :)

[iDaydream00]

This helped SO much -- thank you!

[Teganor]

That's my issue with Calculus. It always seems like just a lot of guessing and making things up to fulfill what seems to be a pointless function/equation. What is the point of Calculus? What is the aim? Advanced math is too abstract. Can someone explain these things to me?

[lifemakesmelaf]

@Teganor hi i know your comment is old but its more of a world application thing. like lets take related rates. on a small scale: if my friend leaves my house without taking her phone, i guess, and i rush into the car to chase her down to give the phone back to her but i dont have much gas left in the car then i would need to know at what rate i am losing gas so i know if i need to buy more and if so how much because i am near broke and calculate about how fast she walks and when ill reach her

[lifemakesmelaf]

@Teganor of course i actually wouldnt do that in that situation. i would just buy the gas later and give it to her the next day or something but if i was doing that with airplane fuel or something really important where i couldnt waste money on unnessary gas or both objects seem to be moving at the same speed but mine is faster. hope that answered your question :)

[lilangel0072]

@Teganor Calculus is awesome...shit load better than having to memorize a lot of stuff like in chem or bio. Calculus is brilliant, sure u have to guess a lot but the guesses are logical, it's a way of keeping your brain working by figuring things out in this way.

[theMDWiz]

@Teganor calculus is used everyday, its basically the "summation"of everything its used to calculate trajectory its used in stores , it can be used to calculate the waiting lines at the amusement parks and even calculate the math of waves of the water. I know its hard but its just something you gotta sit down and try to understand like the other extreme: ..chemistry!

[mpatt79]

@Teganor EVERYTHING you use in your life was made with math. Your precious cell phone, your car, the home you live in involves math, again, everything. It is the language with which the universe was written :)

[ProudSF]

@Teganor I know right? Ever since calculus, math actually made sense... But this guy makes calculus alot eaiser :P

[Hippoman141]

@Teganor take  physics, you will understand

[thingaling827]

thanks a tonne. your video helped alot

[typicalazn93]

this video helped me more than a two day lecture from my teacher... -.- Thank you soOo much

[sade6208]

i cant tell you how much your videos have helped me! thankyou thank youuuuuuuuuuuuuuuuuu

[7863393]

Youtube.. my last resort.

..

Should have been my first.

Thank you!

[rinwhr]

He is left-handed and is he married

[Netjack]

Your videos help alot. Thank you so much.

[incendiastella]

i LOVE ur videos!!! saved a quiz or two of mine :P

[wayofwei]

I just want to thank you for this. It helped me a lot, since my calc teacher doesn't teach in the class (he likes to think that we all understand this perfectly within seconds even though it's the first time we've seen this), and I haven't been getting this down fast enough for me to do well on our quizzes (which is everyday). So, hopefully this can help me out tomorrow!

[greencoveredbridge]

my textbook says that for a limit to exist, it has it be approaching a number. it specifically says that if x , from both sides, is approaching the same infinity, the limit DNE, but you should note the infinity information.

[patrickJMT]

sounds good to me. this is also what i tell my students

[picazitow]

tnx verry much for doing this videos i´m from mexico and this really helps :)

[Aeropchick24]

Isn't an oscillating graph discontinuous also...like the sin 1/x????

[dorothydorothy111]

8 cups of coffee...starting to make sense

[southoreast]

8 cups of coffee? Wow. You're a warrior.

[T4styTHC]

@dorothydorothy111 A bowl works more wonders than 8 cups of coffee, learn from the physicists!

[libardogonzalezalvar]

I just love your classes, they are very helpful for me because you are a person who likes sharing knowledge and that is a very rare characteristic to find in people nowadays

[patrickJMT]

i am glad that you like my math videos : ) i am just trying to help out my fellow human being

[ecaep86]

you should be a calc teacher!

[7ynx]

awesome. \o

[Sm7th]

My calculus teacher used to be a nuclear physicist, but his teaching...yeah.

You can tell he knows it, but he fails to...

pass it on?

I told my whole class about your site, thanks.

[patrickJMT]

thanks! glad the vids help

[jooooooje]

thank you very much your videos are really helpful

[ViadoMundo]

Thanks :)

[jachina]

thank you so much for the video, i really needed it, we're learning about continuity and limit in our class right now, hope for more video on limits!

[patrickJMT]

if you do not see what you need via youtube, i have quite a few hosted through google video! i have links to them on my website!

[patrickJMT]

hey! no pardons needed : ) PLEASE always feel free to ask questions. : ) likewise, i hope i did not sound rude in my response! if you look at the picture, this is what a jump discontinuity 'looks' like. it jumps from one finite value to another finite value. i do not know if i said it explicitly in the video, but from the picture the limits do exist as finite numbers, and yes, this is the requirement for a jump discontinuity. the left and right hand limits exist and are different!

[patrickJMT]

a jump discontinuity is when a left hand limit exists as a finite number and the right hand limit exists as a finite number and those numbers are not equal. sooo i am not sure what the definition of an infinite discontinuity has to do with the definition of a jump discontinuity... that is, i can not determine what your objection is. : )

[superdeejay8]

thank you!

[libardogonzalezalvar]

thank you very much palm. your videos are really helpful, for my classes and personal enjoyment. keep on walking.

[libardogonzalezalvar]

thank you very much

[patrickJMT]

i hope the video and audio quality are ok! got a new camera, not sure if i like it : )