The Squeeze Theorem for Limits, Example 1

[TheNamelessChicken]

How did I get here from Cool for Cats?

[Maydaysdifference]

awesome! the 2nd problem totally helped w/ my hw

[MinnieMouse117]

Thanks! This helped so much :D

[hhabibzadah]

If you don't go to heaven for the help you've provided MAthKIND, then heaven doesn't exist.

[svmgv]

Thanks!

[BelgarionRiva101]

Our teacher was shy about saying squeeze theorem. She said: It's called the sandwich theorem, but some refer to it as the.... well.... squeeze theorem... >_>

[TehRice]

i can't believe this was such a simply theorem, damn my teacher

[CreamPieMyFace3]

i love you

[DaDude458]

thank you. teachers rush to get through the chapters and they forget that we don't know it yet

[patrickJMT]

@DaDude458 teachers get in trouble if they do not cover all the material so they have to rush. it is not something that most of them want to do!

[FallenStar117]

genius

[Yozer245]

Thanks for the video... my teacher never explained it. :D

[MajidEgypt]

thank you very much, your a star !

[nattybro92]

thanks mr mackey

[MrTesticulator]

could you use L'Hopitals rule for the second example also?

[vancruel27]

dude, you are so good haha how old are you?

[MrAustinpowers838]

you suck your video blows

8======>

[john38285]

I'm 12 and with your help I'm doing university math

[mufc4everch]

@john38285 Good job,

[NinjXPk]

WTF: my teacher gave the same examples in class?

[CrazyApe360]

Can you choose any number to multiply the inside and outside limits? For example, could I multiply the outside and inside limits by x^4 then take the limit?

I am trying to find if there are limitations to what I can multiply the outsides by.

Thanks in advance!

[hellobye14]

i love you

[IslandCityPictures]

OOOMG i totally get it now, you're a saviour! my test is tomorrow!

[Ssendecki]

@IslandCityPictures dream on

[123keely456]

I'm so glad that I found your videos! you're great at explaining concepts in a simplified way. I have my midterms tomorrow and I don't think I'd be quite as prepared for them as I am now that I found these! :)

[XxXxXNotoriousXxXxX]

its so simple thanks so much

[imhiLARRYous]

I have a quiz on this in about 2 hours. I fully understand it now, thanks a bunch.

[ericzap]

A lefty writing on a whiteboard? Mad respect.

[angelicmusiclov3]

OH my god thank you saved me from my midterm today!!!



[SeniorSmurf1]

you should replace my calc prof.

[Padfoot333]

The first example is the same one used by my calc prof. o_0 lool, thanks for explaining.

[imahotguybabe]

hey he's a lefty! I heard lefty's are smarter!

[av3ragetomb0y]

@5:10 that little dot ...why didn't u erase it @ n @

but anyways, thanks for the lesson.

-person with ocd

[smokinep]

now i totally understand

[heyyy3210]

I looked at the wedding ring on your finger and i was like... DAMN. hahha jk

[slowmofosho]

in the second example, why do you multiply by x^2? i dont get it



[aaadddaaammm777]

What about a multivariable function such as e^(1/x)arctan(1/y) as (x,y) approaches (0,0).

[dtsuei1]

the 2nd question was on my exam 10 minutes ago

[OhYeAhOhNoe]

i have spent 5 hours studying for a test tomorrow. within 5 minutes of this video i had the biggest "OHHHH THAT'S WHAT THAT IS" moment ever. thank you

[MsDody94]

You are a life savior sir ! ..

[8IceBlaze]

Thnx saved my butt from calculus

[patrickJMT]

@8IceBlaze the calculus butt monster cometh

[framingstanleyVEVO]

thanks man. u make it easier

[IDBC94]

Made it to sleep tonight, and gonna be able to turn in my homework tomorrow because of you. Thanks so much.

[patrickJMT]

@IDBC94 did you dream of my hairy arm? i hope not...

[MrAlexCollins]

You are awesome.. that's tomorrow's class explained! Hi5

[destructo771]

OMG THANK YOU

[wisdomwielder]

Why can't my teacher just explain it like this? This is so much simpler than rambling for an entire hour.

[Scarywesley4]

You should teach my calculus class.

[ryankk44]

Thank You:)

[Arabian1Princess]

why did you multiply specifically by x^2 ? Thanks alot btw, great video :D

[fcballer77]

I <3 U

[NurthinAziz]

i love you! <3

[Florence4424]

Thank you!! It was very helpful!! If I ever left my notes at school again, I know where to get help! ^o^

[Seedgar77]

You are slowly becoming my hero! I try to find this stuff in class and it just doesn't come this easily. Thank you so much.

[MadXChemist]

Fantastic! I thought The Squeeze Theorem would be difficult! Thank You for making this video!

[swimmaster45]

o my god patrick...tyvm you are a great supplement to all calculus assignments and make anything so much easier to understand than the crappy text books

[Richardhuang70]

thank you for your video!! my lecturer claimed that his way of teaching was the only way possible...and that no other way would give as clear a definition. but it's good to find an explanation that doesn't sound too technical and confusing! i think i've learnt even more through this. =)

[DeKorellHall]

Great! I finally get it!!! Thank you!! I wish you were my tutor!!!

[HarvieKevin]

after seconds and seconds of looking at my book, and giving up on this topic at around 20 seconds after listening to my maths tutor blab on about "two police men and a drunk person" LOL, i'm so glad to say i now understand the basics of the squeeze theorem from a 7 min video! i could probably whizz through all my maths problems through mr patrick here, without waiting for my clueless paid maths tutor -_- :D

[fizza78677]

thank you so much :) this video has helped me greatly.

[VOC2006]

I lol'd, you made it seem so simple.



[ClannadForever]

BLESS YOU. 

[oldschool89]

This is simply Genius stuff... i just understood everything i needed to for my midterm... Patrick, number 1!

[srslayerz]

4:59, that awkward moment when there is a small dot that's bothering you

[Blackl3gend]

nice vid... but what if u want the lim of infinity?

like i got a example with

lim n->inf cos(pi*n²)/n²

[Benjikj]

can you do a video on the algebra of limits, triangle equality and other such things! thanks

[tijuanamarisol666]

WRONG SIR! ACCORDING TO MR. CROCKER, 2+2=*FISH* !!!! lol. but seriously, you're amazing. Waaaaaay better than most of the math teachers I've had :) keep up the good work.

[neilcwright]

getting tired of the mormon ads interrupting patrick

[ablast691]

id like to see some more like this !

[plzdontkillme17]

14 people did not take patricks's advice and tips :)

[reddevil16carrick]

@ARQ911 From what I gather you are trying to make that middle term equal to the term in the question on order to solve it. Hope this helped, obviously I can't explain as well as Patrick

[espio142]

OMG, Thank you so much! It helps!!!

[kimpx]

>.< thx alot , completely understand about squeeze after seeing this.

[brownsugrr]

you are a life saver! much better than my math teacher..

[Geishas03]

13 people failed calculus

[jackxzx]

i swear dude you are awesome!

its like God sent you to heaven to save me!!

thank you and never stop posting those videos!

[SonOfNye]

Question, I understand that this is to teach the math of the squeeze theorem, but could we not have done this by inspection since the limit as "x" approaches 0 of (x^2) is 0 and and that multiplied by anything is 0?

[smackdwn23]

youre going to be the reason why i passed MA181

[wswartzendruber]

Alas, it finally makes sense!

[arielalexis2010]

marry me?

[patrickJMT]

@arielalexis2010 taken!

[mrnajowa]

make a mistake in the first examlple

[angelakle7]

Thanks a lot!

[brandibomb]

you teach math better than my math professor in college.

[nekorur]

You are a lifesaver. I'm reviewing for a PDE test, and I had completely forgot how to apply the squeeze theorem. Thanks!

[LindzBeutler]

I used your videos through Precalc and now through Calc and they are so helpful! Still no videos on The Precise Definition of a Limit? I am so lost.

[lawpetex]

hi, can you post a video for limiting a circle function?

[619cyanide]

thanx dude i finally got it....

[Phiba14]

I would say your videos are the best test reviews ever! Thanks a lot!

[warden13]

How do you hold the cam? With your mouth If so, how do you talk? Playback?

[cepson]

You make it scary simple. Good job.

[mmoser2010]

omg i actually understand now! thanks! i go to OSU and all i can't understand my professor at ALL.

[mmoser2010]

omg i actually understand now! thanks!

[ahmad20100004]

guys please answer me how we can now when to use the sequeeze theorem??? pleaseeee i need help in this



[ahmad20100004]

but how we can now when to use the squeeze theorem??

[ahmad20100004]

but how we can now when to use the squeeze theorem??

[eduyntje1]

OMG!

you are a genius pro!

It's so simple when you say it...

Respect!

[matthellenbrecht]

Thanks for the help man. My calc teacher blows, I wish you could teach my class. The infamous Squeeze Theorem has become understandable at last.

[ijoly]

props

thx

[BassDJB]

I cannot thank you enough for these vids. I've been watching almost 3 hours of these vids for my Calc final. I really appreciate it, along with the rest of the YouTube viewers.

[Tijke]

you are my hero!

[PasqualeRinaldo]

how do you do this in a 3 or 4 dimensional problem?

[michies12]

THANK YOU SOOOOOOOOOOOOOOOOOO MUCH! You really did a good job in explaining.

[Dagabe101]

This actually makes sense now!

[98hahelos]

hey dude! marry me! hahahahaha

i loveeeeeeeeeeeeeeeeee your vids. i cant believe something this simple needed to be explained in 1 hour or 2 hours lecture. honestly. what's the point?!

it gets more confusing. not worth it.

lotsa love from malaysia <3

oh, i swear your 1st equation went in last yr's past year exam. not kidding. i have the paper with me right now! lol!

[111000may]

thanks so much, I loved it!!

[alonsan100]

swweeeeett

[Leighton1992]

Thank you kind sir. My prof does not speak english very well so it is very helpful to have someone teach it to me that does.

[hockeymo]

why is it that i understand it when you teach it, but i can't learn it when my prof teaches it?

[jennnyyao]

youre a life saver!!! THANKS A BUNCH!

[GuildmistressDeby]

are the limits of cos -1 and 1 because that is the domain of inverse cos? if so, then would the limit of tan be -INFINITY to +INFINITY?

thanks in advance

[kashmiri92]

omg!!! you are my god, thank youu soo muchh!

i thought i was going to fail my midterm

you are a huge lifesaveerr

thanks again for putting this up!!!

[jeroeniskoning]

mkay?

[j2184]

OMGGGGG i have a mid term next week and was confused out of mind!!! you are god sent!!

[lovelyalicia]

I get it!!! omg!!!! .....ur good :D

[wen609]

potential life-saver you are

[lion40king]

what if it is [x^2.cos^2(1/x^2)]..........??­?

[Idlerock92]

its amazing how simple it seems when it is actually explained properly, thank you mr. patrick!

[woody189]

Great Video. and you have a pretty sexy left hand

[MelonRiver]

you are GOD

thank you, sir

[mendoza604]

props for minimizing the smudges due to ur left hand :)

[kelsaay16]

I am so happy you made this video.

[akorabful]

=O lol

[0807abhi]

great video!

[happymunkee]

i'm using your videos to pass calc this year :)

i have a quick question!

for your first example, it says that x is greater/equal to 0 and less/equal to 1.

how do you know to use x=1 to plug into the two functions to get 3? Why wouldn't you use 0 or 2 (since the value is within the inequalities) to calculate the limits of the squeezing functions?

[jherber286]

@happymunkee because in the problem it states that the limit of x approaches 1, so you have to use 1 to plug in. if im not mistaken, the 0<x<2 is just there as a formality but you don't even use it

[happymunkee]

@jherber286 oh thanks! for some reason i completely forgot about that part. :)

[iniloy1993]

how do you know when to use it??

im having a hard time in keeping track of all the methods...lol

BTW GREAT VIDEO:)

[frumpychicken12345]

You're left handed!

[CandyColors193]

Hey Pat! Thanks for the video. Just wondering if you could help me out here. How do you solve the problem the limit as x approaches negative infinity of (1-cosx)/x^2. Thank you.

[rostand009]

thanks so much you save my life, i have a test on that tomorrow

[midnightstars0]

thank you so much! this is soooo helpful. :)

[shadowfox544]

Thanks for the upload, dude!

[lolshuhuhu]

this is SO!!! helpful

[wwf101]

your videos are so much easier to understand than my calc class!

[wwf101]

thanks so much, this is so helpful

[devilbeaver99]

Great video helped with my math study heaps, thanks

[supppersmart]

I missed about 4 days of AP calculus class, because of your videos i think i just made all the missed lectures in 20 minutes

[MistuhShyGuy]

OMG 7 mins and 13 seconds of this taught me the squeeze theorem better than a whole 40 minutes of my teacher teaching it to me thank you soo much

[nickieee]

Hey, thanks for replying to my last comment, i didnt think you actually would lol.

And as for clearing up the Precise Definition of Limits, i cant speak for everybody, but the thing i have the most trouble with is applying it to problems. For example, proving that a limit is equal to a value using the definition.

Once again, thanks a lot for your hard work, i really appreciate it!

[timrtz20]

patrickFTW thank you man! i'm on my way to the Intermediate Value Theorem, convieniently located in the related videos

[patrickJMT]

@timrtz20 beware of my poor arithmetic in that video! : )

[nickieee]

Hey Pat, maybe i havent looked through all of your videos, but i havent found a video on The Precise Definition of Limits, involving delta and stuff...I really need help on this, and my professor is ...not good lol. I would really appreciate it if you came out with a video on this.

Thanks for your hard work!

[patrickJMT]

@nickieee i do not have a video for that actually... i should make one since people keep asking. i am not 100% on what would be the best way to make it slightly less confusing

[Dankwansere]

@patrickJMT i think the best way to make it slightly less confusing is if you could explain the "Epsilon" and "delta" symbols, why we use it and stuff, cause i think that is what throws people off the most in precise definition of limits because people get confused with those symbols and why they use it. :)

[ijoly]

@patrickJMT OMG i want that video soo much, let me know if you do it

[mas3rm1nd]

you really are a lifesaver

my teacher at school is sooo incompetent

you are my new calculus teacher for this semester!

^^

[patrickJMT]

@mas3rm1nd i have stuff to get you through all of calculus : )

[ExplodingElmoDeath]

this is just great :D

[Recklessfire0]

wow, this helped me greatly with a problem i had for h.w. Thank you so much, you were very clear and concise.

[skuldscarlet]

OMFG! THANK YOU SO MUCH!

I GET IT NOW!

[gpeng123456789]

you are flippin amazing thankyou so much.

you just broke down my hour long lecture on squeeze theorem in 7 minutes!

thankyouu!!

[gpeng123456789]

for the first example arent we supposed to be solving for h(x) not f(x)?

[katris4040]

Thank you so much!

[dc101970]

you are gonna be the reason i pass my exam tomorrow

[patrickJMT]

@dc101970 dedicate your test to me

[Osty722]

@dc101970 me too :)

[VeNGeNCeZA]

Many thanks, this (as all your other vids) is awesome!

[boustanikare]

thank u master of holly calc

[ELDRAGONMESSI1018]

thank you

[MasonMurdock]

Your approach is very helpful. Definitely the most helpful of the Squeeze/Sandwich theorem videos. Thank you very much.

If anyone thinks you go too fast, maybe they're just slow. They should just pause and rewind.

[intelligentwhirl]

Patrick, no words can express how grateful I am I found your videos and the best part is that they're free! You are my hero!

[pgdrums12]

Good lesson.

Question though- For the last practice problem, you are multiplying X^2 by cos(1/x^2). Instead of doing all the work to realize the limit is zero, isn't it logical to think that by plugging in 0 for x, you get 0^2= 0. So you have 0 multiplyed by cos(1/x^2).... 0 times anything is zero... if that makes sense lol

[maniakdusoleil]

Dude...that was way easier to understand than my calc professor!!! Thanks a lot!

[psychophoniac]

well better than my math prof. thanks a lot.

[mypinkdollprincess]

You are the best math teacher EVER! thanks

[eboutros12345]

Thanks a lot dude. This helped me a lot.

[allstarcam5]

thank you

[Grobannela]

Hey Patrick

Is the same explanation for limits of several variables?..

[Godv9000]

I wish I had found these videos earlier. The AP Calc test is tomorrow. Keep up the good work.

[TwoMuchWork]

If my professors could teach like you, then I would get an A and actually understand calculus.

[yea678]

Thank you thank you thank you!!

[Scratchme777]

thank you very much ,,, really apreciate your effort ,,,,

[Danasqu]

thnx !

[amielleima]

thank you so much!!! nice explanation and examples. :))

[ladydfrombk]

awesome tutorial. thanks so much :))

[pinkshoez21]

it was good, just try going a little slower.

[patrickJMT]

then someone else would say: you go way too slow

[kzak911]

@patrickJMT your a beast!!! no you are going at a good pace, if someone says that you are going to slow then they can watch your video again...

[Engin696]

@pinkshoez21 no way you went at a really good speed! you just pause it or rewind if u dont get it

[biggunsbutler1]

@pinkshoez21 , thats what the pause button is for :-)