The Squeeze Theorem for Limits, Example 1

[@sball95]

Everyday, I go to math class with no clue as to what my teacher is teaching me but I have nothing to worry about because you have thankfully made videos for almost everything section that my math course covers (and you give outstanding lessons... even better than the well renowned KhanAcademy in my opinion). Please keep doing what you're doing man - you rock!

[@franklinmurcia1908]

13 years later and this man is still explaining calc better than my professor, thank you so much!!!

[@TheGrammargestapo1]

My hungarian calculus professor told us that when she lived in the former warsaw pact hungary, her and her friends would jokingly call this the police theorum, as in "if you're between two policemen, you go wherever they tell you".

[@patrickjmt]

That's pretty sad

[@rubico1894]

@@patrickjmt your reply makes it even funnier

[@raultorres847]

I don't know if it's only me but I think +patrickJMT explains better than Khan. Thank you so much for your videos.

[@patrickjmt]

i think so too! :)

[@raultorres847]

lol of course you do

[@makemarshall7041]

I agree!

[@shermanmerman4944]

I can't stand Khan. This guy is great.

[@6ii1ii9]

Khan is like those guys from crash course, Dnews and the like. They do a lot of unnecessary talking, stupid jokes, and add their stupid biases and opinions to everything, when all you're trying to do is learn. The kings of teaching here on YT are PatrickJMT, BozemanScience, and Tyler Dewitt. Straight to the point, fun, and entertaining. I wouldn't mind having a 6 hour lecture with either one of them.

[@patrickjmt]

nooooooo! : ) i already am getting about 10 calls and 100 emails a day with questions. until people start mailing questions with $20 enclosed, i probably wont answer many as i work about 13 hours a day already! : ) sorry! the vids are just a hobby... i make $0 from doing this!

[@solaceyes7767]

Not anymore?😂😂

[@thebullybuffalo]

"If you have any questions, send me an email" Clearly didn't have over 400,000 subscribers back in 2008.

[@patrickjmt]

Yep, that is about right ;)

[@Roy51794]

Patrick! I have my final calculus 1 exam tomorrow, and I found out about you only yesterday! You've been extremely helpful so far but I can't seem to find inverse trigonometric functions and limits (for example substituting X-2 with t and so on..) please help me!

[@thebullybuffalo]

Roei raiku rip

[@pursuitsoflife.6119]

@@ValouroverFear Aren't you asking a bit too late?

[@ZoeCalico]

That's two videos that have helped me for this Monday test.

[@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!

[@patrickjmt]

the range of sine is [-1,1]; the other trig functions: tangent, cotangent, secant, cosecant all have range (-infinity,+infinity)

[@numbersinmath8525]

haaa like the respond

[@ericrzaga]

You are finally saving paper!

[@rocaj5559]

I went to class yesterday... and the professor confused me more than anything. I came home watched, your videos SUBSCRIBED! and now I will pass the class! You rock man!

[@sarahequilavez]

Even 15 years later, this video is still helpful!! Thank you so much Patrick

[@patrickjmt]

Glad it was helpful!

[@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

[@gaiusjuliuscaesar9296]

This video was a huge help! I had this exact problem on my test study guide with no explanation given in the answer key, and you explained it brilliantly!

[@cade_trbo6683]

Its wild to think that i was 4 when this video came out. Now its helping me in college calc lol!

[@Mrjustin151]

One possible reason that videos like this work so well for learning is that people tend to zone out to some degree in an hour in a half lecture, no matter how hard they try. Personally I know that I can truly pay attention and register everything in a 7 minutes video, because its only 7 minutes. Focusing for 7 minutes isn't that hard but focusing and being determined to learn for an hour and a half would be exhausting.

[@1fastcubesolver]

You make this so much easier to understand. I have to re-take a calc test because I didn't do so well the first time and I understand everything so much better now. Thank you so much!

[@DanHlrzr]

An hour ago I was depressed over my Calculus exam on Monday, your video has made me a little more optimistic :D

[@fidaimran5802]

its been 11 years since you posted this video, you have explained it so much better than my professor , and as a first year university student taking Calculus. Thank You!

[@patrickjmt]

happy to help :) come back any time !

[@manchez2012]

truth. I have a final in two hours and your videos review everything my professor at Stanford University hasn't taught. Thanks for being pretty radical

[@Agreedtodisagree]

i am proud we have people like patrick in our community who take time out of their lives to do stuff like this. two thumbs way up!!

[@kayeefung6134]

this is the best video i 've found in KZbin concerning calculus and after watching it ,i understand the idea ,thx Patrick

[@tramnguyen237]

OMG my professor made it soooo complicated that I have no idea what's squeezing theorem about!!! You made my day

[@TheZakev]

In eastern Europe we called: The theorem for the two policeman :)

[@patrickjmt]

noooooooooo dont quit! : ) expect to be frustrated almost daily with math... this is something i had to tell myself (and learn the hard way). now i realize it is just par for the course! glad this helped though : )

[@Idlerock92]

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

[@johnholme783]

Simple no nonsense explanation. Well done.

[@h0bohunter344]

You sir made that so simple it was insane, a clear genius at work

[@stephens911]

all of your calculus videos are awesome for reviewing for a final. your a life saver.

[@aparrotslife]

I wish you could teach at my college...We sure could use an amazing teacher who's easily understood.

[@jessygonzalez6164]

you have helped me get through sooo many math classes, thank you!

[@lisa60932]

You make everything so easy and simple to understand. You're getting me through university calculus, so thank you so much!

[@Phiba14]

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

[@Godv9000]

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

[@blindsniper74]

750 people learned how the squeeze theorem works. Reason why im passing calc thanks patrick!

[@youronlyhotgurl]

i just want to cry right now. you are amazing. thank you so much.

[@bustachaina]

omg THANK YOU SO MUCH! Been reading and searching on the web for "help on squeeze theorem" then i found this video after nearly giving up and I completely understand. THANK YOU!

[@tasadar1695]

dude what 5 professor tried to explain but couldn't you just did in a couple minutes. THANKS

[@JaeJean47]

I'm reading my textbook about squeeze theorem for hours and I can't understand it.. and when I watched your video, I was like.. "is that it?" no way! your so cool!!! thanks^^

[@SkateLover151]

oh my goodness! Thanks a LOT for your video! Today, my teacher was explain this theorem and after an hour of reflection, I still couldn't understand the concept of this theorem! Until I went on google and search until I found THIS video! I was skepitical that this would actually help me. And half way of the video i started screaming "I GET IT I GET IT!!!" haha, thanks a lot! I appreciate your help!

[@andy120692]

You are truly amazing.. you never fail to teach, and I can depend on you! Whatever doesn't make sense in my class, you clear it up for me!

[@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

[@j2184]

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

[@maniakdusoleil]

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

[@patrickjmt]

thanks! now if only my calculus students felt the same way : )

[@rk10106]

THANK YOU!!!! I have a test tomorrow and my teacher glazed over the squeeze theorem.

[@greenapplefever]

Great job dude....I got a midterm today and didn't really understand this concept but this really helped!

[@enzonenation]

videos from 8 years ago still help me pass today haha. thanks patrick, your videos got me through high school mathematics! now I'm in uni and I still watch your videos whenever I'm confused about a topic ^__^

[@ChiefStyn]

I cant believe how difficult this stuff seems when I'm in class = LIM = I cant believe how easy this stuff seems when I'm on youtube. Thanks patrick

[@imhiLARRYous]

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

[@iKrackeD]

Recognize cos(1/x^2) when computed will be much different than 1/x^2, therefore you cannot simply cancel out x^2 on the top with the denominator of cos(1/x^2). Also notice how he displayed the function cos(1/x^2) by itself when in the actual problem it was multiplied by x^2. When presented with the inequality -1< or= cos(1/x^2)< or = 1 remember as long as your operation applies to each side of the inequality you may multiply by x^2 in that inequality. Hope this helps you my friend!

[@misaghalaie4310]

Couldn't get easier, i just had a piece of cake!! Thanks Patric!!

[@TillJannah]

Hi Patrick. U've help me out a lot in my maths. I hate my lecture cz i don't understand them, not to the point and boring. Ur videos are clear and u teach well also.Thank u very much!! keep uploading yeah~

[@Bobbarice]

I swear I've passed all my latest exams because of this guy. If I get my degrees I can imagine I'll be thanking him XD

[@Syruscleat]

My Calculus book defines the theorem as "The Sandwich Theorem." In any event I suppose it is the same thing. Well explained. You are U-tube's main Math Squeeze dude...

[@saki-chan5154]

Great, you just make me understand so much things that I can't understand for 2 semesters. All your videos are so good!

[@PrettyMaggiee]

when i was taking calculus I, this did not make sense for me at all. now that im in calculus II, it makes perfect sense! thanks soo much for all the help Patrick :)

[@brownsugrr]

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

[@crunchmandu]

you really are a lifesaver my teacher at school is sooo incompetent you are my new calculus teacher for this semester! ^^

[@wii3willRule]

Thank you, I was having trouble picturing how the theorem would be applied, but this helped a bunch!

[@Deelan1990]

Switching the transcribed captions on for this is always amusing.

[@grahamcromwell4909]

Subbed! This is perfect! Im just about to go write a Math midterm and didnt understand Squeeze theorem and now i get it, thank you so much

[@mypinkdollprincess]

You are the best math teacher EVER! thanks

[@yandisamadinga3900]

Wow now I clearly understand squeeze theorem..Thnx Patric!!

[@wisdomwielder]

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

[@cepson]

You make it scary simple. Good job.

[@MrTwoEyebrows]

If only teachers would show more examples like the way you do, it'd make learning this stuff a lot easier. >.< thanks again man for your calculus help!

[@DreamFist11]

Thanks for your comment that helped me understand limits a little bit better!

[@johnking276]

Excellent video. Not for the content, which (of course) was spot on. More for the way it flowed. There were no distractions, and so my brain was able to follow.

[@museethio]

haha, I couldn't stop laughing when u kept trying to erase that tiny mark.

[@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! :)

[@royiw1050]

You just made it so clear for me. I dun even need my notes right now. Thx!

[@whitneyjordan14]

Thank you so much for this video! My professor did not explain this well at all and now I completely understand it :)

[@andrewbui4287]

So much informative material on this channel

[@patrickjmt]

hope the final went well!

[@Vinnymeister87]

This is extremely helpful. Thank you very much for teaching the masses.

[@rosannaliuski3686]

Thank you so much, you're saving my math finals!

[@1Rab]

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

[@Henripped]

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

[@R0WD1E]

Thank you for showing step by step!

[@loveisloveislove13]

thank you so much! i have a test tomorrow on this stuff and i didn't get sandwich theorem until i watched your video... thanks! (:

[@nathanthursby1471]

awesome vid, by the end was able to understand them suffiecently compared with 2 hours of lectures keep it up!

[@MsDody94]

You are a life savior sir ! ..

[@joelfloren6306]

Thanks man, you broke this down perfectly. I understand it way better!

[@eduyntje1]

OMG! you are a genius pro! It's so simple when you say it... Respect!

[@KissieSweets]

You're the reason I'm going to pass my midterm today

[@AxeRingingThrasher]

THANK YOU! midterm today lol u saved my life

[@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. :)

[@crimeluver]

THANK YOU SO MUCH!!! I was a little confused on one of my calculus problems, which was prove how the limit as x approaches 0 of the square root of x cubed plus x squared times sin of pi divided by x equals zero, but I finally understand it! :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.

[@coolshit629]

Thanks alot! really cleared up alot of my calculus confusion

[@AltanProject]

Thanks man! I've a midterm in 2 days and it helped me a lot! good job

[@Twyant2]

Why can't you be my Calc teacher!? Your videos make everything so much simpler!

[@kenlu9968]

Thanks for explaining this concept so well! Math doesn't come very easily to me and these videos are really helping me in class!

[@patrickjmt]

glad that you think so : )

[@gBakos126]

Hey thanks so much man that really helped me, I had no idea what my teacher was explaining, you're great at explaining! God bless

[@fezdispenser]

Thanks so much for posting this. It was a very clear and concise explanation; especially the example at the end. You are awesome!

[@gian2g]

Sweet thanks man! The squeeze is easy but it can be a pain when it comes to using like you did in the last example.

[@debbiehannam974]

I liked your sandwich theorem explanation. Are there identities to use for 1) lim ((x+sinx)/(x+cosx)) as x app infinity? 2) lim ((3x^5) /(e^x)) as x app inf? 3) lim ((5^x) / (cos5x)) as x app inf? or do you have to look at graph to solve?

[@MadXChemist]

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