Continuity - Part 2 of 2

[djumr]

hey Patrick are all the polynomial and root functions continuous at the given ranges?

[patrickJMT]

@djumr they are continuous on their domains, yes.

[hedgehogsamurai]

Dude, I like to thank you for the help. I managed to pass my class after watching most of your videos that made some of the concepts easier to digest. Once again, thank you.

[andreirocks1992]

i would subscribe twice if i could :)

[patrickJMT]

@andreirocks1992 hahaha : )

[drdp15]

Most of my class are using your videos... Thanks so much on their behalf and mine but my question is will you be doing a video on Rolle's Theorem, I ask that you do if possible :) Thanks very much again

[biggregpopa101]

hey patrick gotta quick question..is x^2tanx continuous everywhere?

[patrickJMT]

@biggregpopa101 no, but it is continuous on its domain

[PaulieCrous]

hahaha. love how you held back on "obviously"

[patrickJMT]

@nana7937opooku probably never

[luisespanola]

"jump dis"

[MsLuLuJordan]

@patrickJMT

u made my day dude :)

i have a question though, u said that it is a jump continuity because the two numbers are finite numbers, how do we know when it is a removable one?

[patrickJMT]

@MsLuLuJordan it is removable if the limit exists, but it is not continuous

[LlamasWithAtaris]

The whole video I was praying you would have a function with three pieces. I jumped out of my seat at 4:08. Thank you thank you thank you! 

[patrickJMT]

@LlamasWithAtaris ha, happy to help : )

[v1ruzspawn3]

no MATTER who has the most views i always look for your vids.

[patrickJMT]

@v1ruzspawn3 thanks ; )

[LAnonHubbard]

Thanks

[tapaddtiiiii]

I will name my first born after you

[patrickJMT]

@tapaddtiiiii patrickjmt will be a funny name ; )

[StitchesScreens]

i still don't get it

[mojache3]

you're awesome

[dakboyyall]

Thanks a lot for these videos because i need a lot of help with calculus this semaster.

[chyeahhxkaity]

Thank you SO much.

[WindBreaker77]

UR THE BEST!! 

[natash179]

Can you do some more examples?

[natash179]

I wish you were my professor. Thank you!!!!!!!!!

[Chuyssbb0wner]

Why did you pick f(-1) and f(1)?

[BorealNeal]

this is way better than what my prof teaches us for example on the first day of class:

prof: ok class so when f(x) is equal to g(x) than the f(x) value is the same as g(x) is g(x) is only equal to f(x) sqaured making g(x) the f(x) of all reals and that g(x) is the f(a) of lkpty 4.555666666666 and repeating ok any questions?? good lets take a quiz

me: -.-

[iheartmozart13]

thank you!!! great jjob explaining things! you are WAY better than my teacher..

[TheNumber2Pencil546]

can you do an example that isnt a piece wise function?

[Rockingal189]

Thank you for saving me. ^_^

[TonWiff]

thank you Patrick....you're the best tutor ever....THANKS a lot :))

[tkatiqah]

I LOVE YOU SO MUCH! XOXO

[da1booger13]

My good man, people like you and Khan from KhanAcademy are truly worthy of admiration. Because one, you have a beautiful skill (Mathematics) and two, you don't keep the knowledge to yourselves but you share it to the world for free.

Well done and Thank You Patrick.

[emilygoat]

i love you. thank you.

calculus makes me cry.

[krai999]

4 people failed there exams

[ian559fresno]

Awesome videos, hopefully adsense pays you decently for your time :)

[TonyDog360]

Hi, amzaing video! I have a (hopefully) quick question, in the second example you found where the function is discontinuous, how would you express where the function *is* continuous in that example? I did a similar question, but we're told to find where it is continuous as opposed to discontinuous. Or is this method not correct for finding where a piecewise function is continuous?

[Ichimaru666Gin]

thank you so much for the videos:)



[TheNumber2Pencil546]

you are the best tutor on youtube. and you almost have 1000 vids! nice

[patrickJMT]

@TheNumber2Pencil546 thanks : ) yes, i have spent many many hours making (free!!!) math videos

[zeeshan3dge]

@patrickJMT every one like (free!!!) word but here it means (invaluable!!!).

[lmafo4utube]

@patrickJMT if i was rich i would pay u if that makes you feel better XD

[persiantube1990]

@patrickJMT just out of curiousity, do you make a lot of money out of these videos? --> a friend of mine has just become a partner and if it is good than I want to make videos also... you dont have to answer it if you dont want to but still...

[Munchpooh]

Thank you so much! You explain it so well. Could you please do more example?? Thanks

[Munchpooh]

Thank you so much and could you do more examples please!! Thanks

[jackxzx]

please patrick

more examples : (

[JayKwik69]

Why can't you teach my calculus class... well you're youtube channel is almost just as good so thanks you kinda saved my life... since my calc teacher can't teach or just refuses to teach

[Dethisme6]

Hey, just wanted to say thanks. Your videos seem to be helping me a lot, I've watched part 1 and 2, I seem to be getting the correct answers. Great videos, keep it up!

[messiahjonz]

Your videos help a great deal, I recommend them to my fellow students.

thank you.

[Abdallah0822]

youre soo awesome bro, YouTube education is the best education ever.

There's many inefficiencies with regular education in the classroom. I love YouTube videos cuz I can press pause if I miss,something, press pause and copy down an equation or graph before you talk and listen carefully..... nothing I can do in a real class where Im scrambling write down what he says and listen at the same time.

[shainaiswhoiam]

Heeeyyyy!!! You are MY HERO!!!!!!! :)

Can you do an example and/or definition of nonremovable discontinuity???? My book has it and I dont get the difference... or why it is nonremovable!

[punkojosh]

I swear matey, you are the sole reason I am passing my degree. You should come to Keele in England and become a lecturer!! :P

[arcanapanda]

my gosh.. Thanks so much! if i didnt watch ur vid, i'm sure i'd fail my exam tomorrow. tnx a lot!! 

[michgee]

This helped A LOT. THANK YOU VERY MUCH!

[Kingboy676]

thanx شكراً

[MKhanna6396]

Heyy, thank u soo much for the post, extremely helpful!! :)

though i had a question, how do you show that a f(x) function is continuous on a interval? and, how would you do answer this : Sin x/3+Cos x?

if you could please help me with that, would really appreciate it!! :)

[izzasa666]

plz sum1 explain to me in the first example how can u say 0 is the only possible value whr x myt be dist? its x greater than or EQUAL to zero!

[pithikoulis]

@izzasa666 could answer if I understood what you type. whr? myt? dist?

[Heathaa369]

how would you do these: y=cosx/x and |x-1|+sinx ... How do you show when they are discontinuous ?

[blueyblubber]

thank u mr.patrick

just a question thou

i still dont understand where u said

"the following functions are continuous on "their" domains"

dont rly understand what u mean

[sarandrea12345]

I have a question. What if a function is continuous everywhere when x does not equal, say 7, how do you find the value of f(7)? For example, If the function f is continuous everywhere and f(x) = (x^2 - 25) / (x - 5) when x does not equal 5, find the value of f(5)?

I have looked at every calculus video out there and I can't find any help.

[patrickJMT]

@sarandrea12345 f(5) is undefined because you are dividing by zero. it is not any value.

[SLTalent]

@patrickJMT isn't that just the indeterminate form? I thought the answer would be 10 as (x^2-25)/(x-5) = (x-5)(x+5)/(x-5) = (x+5), subtituting x for 5 giving 10?

[rwtfallenjf25132]

@sarandrea12345 i thought u would factor the top, cancel out the top and bottom, then all that u would have left would be x+5, then f(5) would be 10, or is that how u make f(x) continuous at f(5)

[grunt2382]

@sarandrea12345 I believe you have to simplify the numerator first, which will be (x-5)(x+5)/(x-5). From here, x-5 cancels and you're left with x+5. So, in this case, f(5)=10.  I'm pretty sure this is right, but I'm still learning as well. Hope I helped, even though your post was from a while ago.

[ricsurfpro]

I hav a question in the sencond expaple you show a function that is continuous but hav 2 points of Discontinuity ??? or the function is  Discontinuous and hav 2 points of Discontinuity ?

[patrickJMT]

@ricsurfpro it is continuous everywhere except those two points which are discontinuities

[ricsurfpro]

@patrickJMT you are nice =D you help me a lot whit my Calc 1 test thanks !!

[erikationofkita]

good vid! have you made any videos on differentiability by any chance? if so please tell me what they are called so i can watch them i need all the help i can get! thanks!

[breana95]

This is just wonderful! if i had an online class with calculus, i would just come here and i would totally understand. professors make everything seem so dang hard when its not

[HiyakapuaGaming]

Got a test on this tomorrow and these videos are helping a lot! Thanks, and subscribed!!!!

[vaughnn24]

good sir, how can i graph the parabola by derivatives?

[blahlalaify]

why can't textbooks or teachers make it this simple??

Very Helpful!

[888ryuzaki]

it helps a lot..thank you so much. i didn't understand it before but i guess i am now.. :D

[caryash]

thank you LOT!!!!!!!

[MrOzyDesi]

Extremely helpful video. Thanks a bunch, mr. Patrick !

[patrickJMT]

@MrOzyDesi no problem

[blaqorchid]

Thank you sooooo much for these videos!! You've really been a grade saver!

[supermadcrazy]

hey it was very helpful........i will be verythankful to u if u upload a vidio on geometrical meaning of double derivative............like single derivative is a tangent to the curve at that point but wht the hell is double derivative?????????????????

[patrickJMT]

@supermadcrazy second derivatives have to do with concavity of the graph... i think i have a vid about it already

[blkstarr826]

Thanks! Do you have any videos that show how to find the values of A and B so that the function is continuous? Those always stomp me.

[meker123]

O for Awesome!!

[kapranoshw]

Thank You it did help =D

[xxsumanxx]

Absolutly brilliant! so much clearer now!! thank u

[aad1236]

when is f defined

[thamariyalfb]

what's an essential discontinuity ?

[aparrotslife]

Thanks a gazillion.....you're awesome...:)

[iMNice99163]

You da man!

[makeupandshoes]

again, thank you SO much for this video. This is amazingly helpful for me...my teacher is BRILLIANT, but she's Japanese so I can barely understand her.

[djcrono]

Why are we using 0 when evaluating the limit from the left (2:30)? Shouldn't we be using a number less than 0 from this side as the other limit (from the right) is for numbers greater than or equal to 0?  I hope that made sense...

[DoxieDaddy62]

I was confused as well when I first was watching this video, but after trying the problem out for myself (with values less than zero), I found that the limit, as Patrick says, is zero. I wonder if he was just saving time.

If I'm completely wrong, I'd love to know so that I too can understand this better.

[kronos189]

thank you my friend

[moonlightkitten]

Do you realize how essential your videos are?? I did not get one word from my teacher until your videos sent from up above

[okbalgo]

@moonlightkitten I KNOW...he is great.

[ThierryHenry140]

very helpful patrick, thank you so much!!!

[arieljohn]

Thanks Alot Patrick! Your examples were really useful.

[AirlesMan]

Would you like to give some more examples on exponential functions please?

[niruzzz]

What about points of discontinuity involving open/closed intervals? I dont understand those in the least...

[dual85]

You are a terrific in supplement to my classes. I can't thank you enough.

[DarklightALBANIA]

@dual85 Like protein shake after gym

[FaiththeHairstylist]

Patrick, this video was very helpful! I've been very confused about this topic.

[andy120692]

at 1:10, where did you come up with that disc = 0 part?

[MrWyte1]

I want shake your hand! Thanks!

[newdude50]

Thanks for this interesting lesson on Continuity. It was a nice review of continuity. Are you going to cover more topics in calculus through your videos? (like derivatives and integrals)

[halfbl0edje]

how to make them continous?

[mami406]

thank you very much..but PLEASE MORE EXAMPLES

[Stephaniejay90]

For the first example, can you just say that because lim x-->0- (x^2+3x) does not equal f(0) then the limit does not exist?

[phebes2009]

f(x) approaches a different numer from the right side of 0(lim x--->0+ is = 1) than it approaches from the left side of 0 (lim x--->0- is = 0),thus, limit does not exist

[phebes2009]

Also,

according to shadow and Patrick's video (continuity Part 1 of 2), example 1 is one of the types of discontinuity called jump discontinuity.

[phebes2009]

your explanations are a lot better than textbooks

The first example is similar to the question from the exam I just took. The question is: this function is not continuous because :(Select only one answer) : (a) limit does not exist (b) limit on the right is not equal to limit on the left.

I chose (a) because this is one of the definition of continuity of a function.

Patrick , pls let me know what you think.

[shadowcat913]

it should be (b) because it's jump discontinuity... the limit still exists

[patrickJMT]

well, the limit does not exist : ) it does from the left and right though : )

thanks shadow for helping!

[versusboop]

thank you so much!!! im glad i can count on thiS! im all the way in argentina lol

[rashk1]

Thanks for the Video

[marijo790]

Do you have any videos on the neighbourhood of a point? It really confuses me. Thanks your videos are great, you're definitely saving me

[patrickJMT]

no, but the neighborhood of a point is any open interval containing the point....

[1a1a2a3a]

So the for the first example, what were the discontunities if any?

[dread205]

What if the example was about 3 piecewise functions like the second example in your video, but I had to find constants such as 'a' and 'b'

after I find any discontinuities, how do I solve for 'a' and 'b'?

[Raven10]

What the hell?!!! so this is what the class was about?!!!!! Oh my god thank you so much!!!!=)

[patrickJMT]

ya, piece of cake : )

[1a1a2a3a]

ahahh!! I loved that comment

[syeda05]

=O I LOOOVE U MAN u saved me from failing my first test tom!

[patrickJMT]

you have to write: the test is dedicated to patrick at the top of your exam

[syeda05]

LOl shuure =P

[msdesai]

You should be a professor

[IGOTCREAM]

thanks a lot, you just saved me!

[PhototropicLemon]

this is simple

[patrickJMT]

that means you understand it

[PhototropicLemon]

yes :)

thanks

[mi302]

THANK YOU!

[parastish270]

Thats cool,

Hey you doing great job, May you have success everywhere in your life.

[patrickJMT]

thanks my friend : )

[ViadoMundo]

Hi Patrick! Thanks again for the video :)

[patrickJMT]

no problem VM!

[Zatono13]

I LOVE YOU.

[patrickJMT]

nice! : )

[wynrick1]

how do you know what number to start with when checking for discontinuity? In the first example you use 0 and then in the second one you used 1. Why?

[patrickJMT]

it depends on the types of functions you have as to where u look. my functions are all continuous on the given domains, so they only problem is potentially at where the functions switch, which is at x = -1 and x = 1, so that is where you look!

[fleepss]

THANKS :]

[rachellej89]

thank you so much, honestly you explained this in a way i could understand it. hopefully i'll do well on the exam tomorrow.. again thank you and i'll most definitely come back for more help if needed

[patrickJMT]

good luck on the test!

[MundusLitterae]

I have a test today on Limits, Continuity and derivative but thankfully, I went over your examples and I remember continuity now. Thanks a lot!

[BIGdadei]

i got some questions if i may. what exactly is a limit? is it like an asymptote ? what about trigonometric functions? like if sinx as its limit approaches infinity it would be undefined because it oscillates? also do you have any videos of limits of divisions(in general as well) being radicals on the bottom (more precise square roots because they come out more often) ? like and last question do you have any tips on how you know when a limit is going to be an infinity symbol or an actual number?

[patrickJMT]

you asked a lot of questions! i have videos on my website that describes all of this stuff. there is no way i can give a concise answer to all that stuff : )

under the limit section, there is videos that describe the basic idea, along with lots of examples.

[BIGdadei]

ok thank you very much. but do you mind if i get the links to them. i was going to ask you sum other questions but it was late and now nforgot them. thanks though

[InternetLoveMachine]

Thanks man, but would you write that final answer on the last example as removeable discontinuity at x=1 and x= -1, or nonremoveable discontinuity?

[patrickJMT]

it is nonremovable. since the graph 'jumps' you can not somehow make the graph 'come together' (that is: be continuous) by simply filling in a single point. imagine though, that the limit existed but was not equal to the value of the function there. if you make the value of the function equal the limit then now you have removed the discontinuity and the graph becomes continuous... (at least in regards to my graphs!!!)

[InternetLoveMachine]

all right, that makes sense. thanks again :)

[crymebeast]

dude thanks 4 the examples but can u show certain questions with modulus....and trignometry.....like sinx cosx sin|x|....so on

..even functions involving log...and few fractional sums....nice work anyways.

[JewVol]

Thanks man. My math teacher is beyond horrible.