Limits Involving Absolute Value

[WondersSilent]

I feel like I learn so much more here than in class....

[patrickJMT]

@WondersSilent keep coming back to watch in that case :)

[WondersSilent]

@patrickJMT I already am :D

[sl33pin1nschool]

I didn't get it when my teacher tried to talk about it, but you made it so much more clear. Thank You.

[battousai12345]

Thank you! My calc professor just writes down equations without explaining the intermediate steps of those equations.

[NuckMyFuts352]

Marry me? I LOVE you!

[Springerdude11]

Great video! Helped a lot!

[ru2dumb4school]

I was working a problem that was absolute value of theta over theta as theta approaches for from the positive direction which of course equaled one. But then the answer to problem asking what the limit of theta was from the negative direction did not equal negative one. I can't find the answer, can you help? lim |theta|/ theta  theta approaches 4-

[maoomph]

Wow you made it so easy thanks, you helped me more than my teacher who keeps rushing every lecture we have.

[Rondo205349]

you said "shit" @ 9:43 hehehee

[orton220]

Thanks! You helped alot. I will definitely be viewing your other videos

[patrickJMT]

@orton220 glad you liked this. you may also check out the playlists if you are interested

[SYKGC]

@patrickJMT

lim x -> 0+ (From the right hand side) (|-1+h|-1)/h

The answer comes out "negative infinity". But at the back of the book it is "-1"

Is my answer right or the book's?

[aftab7471]

can we say that in general limit does not exist for the absolute values????

[cglg1234]

my teacher sorta zoomed over absolute value and i ended up getting marks off this question on a test. now i understand what I had to do. thank uu!

[windmanp]

Thank you, very good solution. :-)

[SInnerMario]

why can't we just put the -0 in the x at the beginning of the second example and say its : -1/0 -1/0 which equals - infinity -infinity and that equals -infinity ??

[7595012na]

thats a clear video!!!

[ROxieCHicks]

i love you, i'm not kidding

[robrobbyrobrob]

could you do a vid on the derivative of absolute value functions?

[MissCherie07]

I love you.

[Mel050991]

hi..what if the X is squared???=)

[MrUndacovabrova]

You know, I used to think the educational system was in shambles up until college, where dedicated professors built up the intellectual integrity of the individual. BULLSHIT. I'm in college and PatrickJMT has succeeded where teachers who are paid handsomely have failed. And IT'S FREE. Thank you, you've saved me from failing my finals :)

[Akirabone]

Wow, :) i understood you more than my teacher.

[Jehanzebxkr1]

hi can u solve some examples like lim┬(y→0)⁡〖7y/(|9y-4|-|9y+4|)〗­im still having problems with these, thanks

[MrUndacovabrova]

@Jehanzebxkr1 I know the answer to your problem, I'm just not too sure how to convey it. Ok, you do what Patrick said about splitting the absolute values. You do it with both absolute values. Then you solve for the limit as y approaches 0 from the left with the negative values of the abs. val. You do the same as y approaches 0 from the right. IF I did it correct your answer should be negative infinity.

[libyanrebel99]

An ad in the MIDDLE of the video???-------ARE U SERIOUS?

[ratifyequality]

@libyanrebel99 Mine was Chuck Norris (y)

[vnsnatera]

For the first example, what would the limit as x approches 0?... Would it still be DNE?

[KeishaSam16]

Thank You so much for your help you taught me how to find the limit when dealing with absolute value how I can break up absolute value into 2. All The Best Thank You. Keep up the Good Work.

[TheEthnikman]

Thank you!

[ICOD73]

Does absolute value limits does exist all the time?

[babboomcish99]

Love this guy

[khinlin]

You teaches us well, do appreciate and I subscribe it.

[patrickJMT]

@khinlin glad u like the vids ; )

[heyyy3210]

Don't stop making these videos! You help a LOT of people!!

[ruzzroozx3]

@timrtz20 OMG so true! i was just about to say that these people are so much better than my professor at school... YOU GUYS DESERVE TO BE PAID MORE! Thanks to you I was able to solve this problem right on my online homework thanks!!

[urcool425]

you're math videos make me love math like back in middle school days...cant find IVT theorem and Squeeze theorem stuff though.

[patrickJMT]

@urcool425 both of them are for sure out there, just do a search or look in the calculus 1 playlist on my channel

[Alexhauser23]

@timrtz20 Agreed 100%, I've experienced youtube being more effective than paid schooling (I'm in college atm) with a myriad of subjects, including programming, game design, piano, guitar, and now math. Dumping more money into education accomplishes nothing, the administrators just get higher pay as a result of that, what we really need is to bring consultants from the new tech-savvy generation in to reform the education system up to today's standards.

[patrickJMT]

@Alexhauser23 you all are the future. get involved, don't be onlookers! that is how the world changes.

[SynpaticInc]

You are amazing. Thank you so much. I've been supplementing my Calc I course w/ your awesome videos. You're an amazing teacher!!

[patrickJMT]

@SynpaticInc thanks ; )

[aceofspades6279]

great video many thanks

[iluvbigbootie]

im not so clear about why the absolute value equaling two different value, but im thinking it has to do with the distant from zero on the number line. like absolute value of 3 is 3 unit from zero and the unit can come from negative 3 and positive 3. Is this the reason why? please help

[patrickJMT]

@iluvbigbootie i am not making it equal two different values, i am simply rewriting it as a piecewise function

[immaeatchu336]

Thank you so much for making it a lot less complicated.

[EnjoyMoosic]

This was extremely helpful! My teacher has a heavy accent and I it difficult to understand her at times. Thank you very much. (:

[Beekster13]

This is amazing and very helpful....thx patrickJMT

[GoodyearBandit]

@timrtz20 I'd rather go to patrick's school.

[terrrriyaki]

VERY HELPFUL. THANKSSSS !

[themoreeyeknow]

That was very helpful! Thank you so much!

[TheMimi1984]

For the last one, I have the exact same problem in my book but the answer is DNE vs. yours -infinity, WHY?

[patrickJMT]

@TheMimi1984 dne means it does not exist as a finite number. infinity is more descriptive than to say dne.

[iluvbigbootie]

@TheMimi1984 the limit is dne because as x>0- and x>0+ are -infinity and +infinity respectively, thus the limit is dne because it didnt approach a single unique number by definition of a limit.

[salim300]

bless you man...............thanks

[egancaubang]

You've got me confused for a minute why did you had a LHS and RHS test on your first example and only had LHS on the second?BTW awesome vids :D my instructor does not make sense.

[Noremae]

i like your reflection...

[MrXenitha]

5:28 who's coughing in the background?

[inmotion86]

It's gonna be a shit... I mean a stretch. hehe.

[zolenaqq]

much clearer. thank you!

[muziccmagnet]

you are such an angel dude keep posting great explanations and more complicated examples

[saniyeleenatalie]

Patrick, I love you



[FuneralMarky]

9:42 "Its gonna be a shit..."

[ccsstorm]

Nice eraser you got there !

[circasurvive04]

thank you so much!

[EpicAlaskanCod]

I just learned what my teacher was trying to teach in a whole class in 10 mins. I love you

[Dave0riginals]

penis at 6:28

[eowdaoc]

hrm i thought the limit of a constant over x was zero? like when you divide the function by the highest power of x

[eowdaoc]

my name is sergio sanchez, and i am a mormon

[zkinnikz05]

A great help! thank you very much! :D

[dukamos]

how can 1 and -1 be DNE ? can you not have a lne from the left and other from the right and find each other at 1 -1

I fail to understand why we have to puts signs or even transform completely the numbers using other techniques? why can't we just replace the X with the number proposed. specially never saw real life examples of this kind of limites. why we study them and what differences it makes.. in people lifes. is merely decorating other peoples formulas. don't even make sense.

[ablast691]

yes i would like to see some more complicated ones like this but this was great!

[codenameBM]

Thank you

Thank you

Thank you

Thank you very much

you are great

[SamYeow2102]

hey! i can see the reflection of your face~

[OpsTeam14]

Did Youtube really just stop me in the middle of a video to show me an ad about a crappy juke?

[prathijamusic]

thank you for being a little bit more thorough :) Ive been confused with this for a while

[sushlet]

Finally, math I can understand. Damned Russian teacher...

[zombieslaya822]

this is math...

[mekbarbie]

I'M CONFUSED. Why do you have to take the limit of the left AND right?.. or HOW did you know that you had to?

[AlwaysBeMyThunder21]

This was great! do you hace a video that explains how to find limit of number that are squre roots but also not fractions?

[vyhuynh1994]

thanks your video help.... one question though as i learn to find the limit i dont know what it is and what is the limit use for ... is there like a real life example ?

[zo0yoRk69]

Thanks man your awesome. i would like to see another vid with absolute values tho im still having some trouble with them. maybe slightly more difficult?

[tcrens10]

Your videos are so helpful! 

[WHY70122]

1st of all, i appreciate for whatever you've done for YouTube cuz all of ur vids are priceless. I've learned a lot from ur vids.... but if you get a chace... plz double check the 2nd example in this vid. cuz ur answer is totally different from the one in the text book (calculus). It should be in chapter 2.3/ question # 43. it gives us the answer like "the limit does not exist". but ur argument is still so logical though...so im confused what the point is... plzzz help... thanks

[mynamewasalreadytkn]

@WHY70122 infinity is more descriptive way to say limit does not exist.

[cavendysh]

Please Help me to Solve I am in disagreement with the Solution.

lim 1 - |X|/1 - X

x->1

[zankou39]

I thought lefties were supposed to be good at art, not math!!

[sparklingangel195]

You should come in and teach my calculus class.

[kuges08]

THANK YOU SOOOO MUCH!!! this makes so much more sense!! :D

[kelslynnx3]

what about lxl/-x lxl/-x lxl/-x

x-> 0+ x-> 0-  x-> 0

I know this one isn't as complicated but it's still confusing me. As x approaches 0 from the right is the answer -1? and as x approaches 0 from the left 1? I know that as x approaches x it DNE.

But your video was very helpful thank you so much!

[juanpatc9]

thaaaaaaanks!



[gengen23100]

THANK. YOU. SO. MUCH. FOR. ALL. THE. VIDEOS. You are so awesome!

I have my Calculus I exam on monday and my prof is not any help at all but you are the complete opposite of him. How I wish you are my math prof. I cannot thank you enough for all this videos and I mean it. I'm very grateful for all this and taking your time out your busy schedule to record them to help millions of students who have useless, crappy teachers/professors! THANK YOU AGAIN!!

[JoshBuntu]

why can't my calculus professor teach like you? why?

[silbersteinable]

@JoshBuntu He's paid to make it seem difficult.

[Ericseaverns]

how do you know when your answer is gonna be infinity or negative infiniti, like the first problem you did, how come it couldnt be an infinity or negative infinty answer like the second problem you did. Like how do you determine when your answer will - or + infinity. Also, why didnt you approacch x from the left and right on the second problem. Thanks alot if you can help me on this. This is my bigest problem.

[damdiramdam]

@Ericseaverns

you won't know unless you try solving it. if you get an answer that has a denominator of 0 but a numerator of a real number then you would have an answer of infinity or negative infinity. in the second example the given stated that x will approach from the left so that means you don't need to get both sides already. hope this helps.

[gdbb5]

thank you for your explaination but can you do one with expansion mixed with absolute value.and can you also do one with trig equation mixed with absolute value.thank you so much.

[alreadytakenthe3rd]

Just to let you know, the derivative of the absolute value of x is the sign of x.

[cjabk]

what about lim x->3- (x approaches 3 from the left) of 1/abs(x-3) ?

how do you solve this? i get it up to breaking it up like a piecewise part

but then i get lim x->3- 1/-(x-3) then what do i do next?

[xLovingxYouxMorex]

Ahh, Thank you thank you! I can't thank enough. I'm in grade 12 doing a university course... This helps greatly. :)

[AlaaYahya92]

i hope you be our math teacher.. i'm an engineering student and i'm facing a serious problems with our math doctor ! :\

[kaye0833]

I'm in grade 12 Calculus..didn't really understand the concept of limits.

and then i watched this, Thanks!!!!!!!!!

[lyj41]

Can anyone please explain to me how l x l = -x when x<0?? I thought whatever value you plug in, absolute value is always positive... Thakns

[meeponline]

Also, how do you find the limit as x approaches infinity, if the limit is a finite value?

[meeponline]

How does the limit 'not exist' if the left limit doesn't equal the right? Doesn't that just mean theres 2 limits, one for 1+ and one for 1-?

[xLovingxYouxMorex]

@meeponline For a limit to exist it must equal the same from the left and the right. :3 There's separate limits for the right and for the left, but not for the number itself, since it's undefined and perhaps a open circle instead of a shaded in one. :3

[kakajunk]

si 2/x has of negative infinity according to the video , is that the same as saying that limit does not exist ?

[kakajunk]

the limit for 2/x is negative infinity . is that same as saying that the limit does not exist?

[jbabe521]

helped me so much! i've got a calc 1 test today. i feel better now!

[fijiwater241]

these videos are helping me pass calculus THANK YOU!

[CBVideofy]

Great job at making it clear!

[sugamocha26]

THIS VIDEO WAS SOOOOOOO HELPFUL!!! THANK YOU =D

[vaj64]

Thank you , sir . for ur lessons in limits and calculus they are vry gud.

I understood every thing.

Sir i wanted 2 ask wether referring g b thomas calculus Pearson publisher would help me or not?

[hollistergrl4192]

i am currently taking calculus in college, and i wasn't expecting it to be so tough... thanks for the great explanations, examples, and overall, WONDERFUL video ! :)

[zeldadu09]

At 2:49, why would one of the piecewise function parts be x is greater than or equal to 1 and not x is less than or equal to 1?

[iFckenLOVEyooh]

Thank you! :D!

[Chrustay177]

hell yea lefties.

[fuzzyclouds]

THANK YOU FOR EXISTING

[gnorihs]

Hi,

What happens if x tends to O+ ?

[gnorihs]

Hi,

What happens if x tends to 0+ ?

[ahs08c]

im looking at a problem with lim X ---> -1- involving an abs. val of x. im confused about making the domain because there are still negative values smaller than 1 that would make this negative. would you just choose a + number bigger than one to make that true? im not sure if this question makes any sense... :-/

[nicbling]

HEY thanks so much for these videos, im so grateful for people like you putting these up to help others. thanks alot

[superaznism]

thanks!

[vip0IR]

so does it mean that whenever we have an absolute value as x approaches C then function doesn't have a limit?

[patrickJMT]

@vip0IR no, it does not mean that at all. it just depend on the functions

[MarvelsofaLifetime]

@patrickJMT: Would it be alright to say the limit is "undefined" instead of "does not exist"?

[patrickJMT]

@MarvelsofaLifetime yep, that would work too!

[nancybobancy101]

I was stuck on a limit problem with an absolute value. Then I googled it. Then I found your video. I just wanted to thank you (:

[patrickJMT]

@nancybobancy101 u r very welcome : )

[thedeviledrose]

thankx lots patrick!!! u don't now how much u've helped me understand calculus ^^

wish u taught in ACK... do u have a phD in math?

[patrickJMT]

@thedeviledrose no, no phd. i did a year of phd work and realized i have no desire to be a math professor, so i dropped out

[shohna]

@patrickJMT Then the world has lost a great math professor. You're a brilliant teacher. Thanks!!!

[MattyHild]

@patrickJMT

So that means you must have a masters or bachelors of pure mathematics?

[patrickJMT]

@MattyHild masters, yes

[MrLonghorn1000]

Very helpful! Much appreciated

[samuel91222]

great explanation...i always stuck at doing this kind of limit..

[JaviAirForces]

damn! this was exactly one of my homework problems! thank you so much, I not only got the answer right, but I learned how to get it correct. Thanks.

[kushirokid23]

That was so helpful! My mind is at ease for my exam tomorrow. haha.

[davidrpo20007]

Thanks, this made it a lot more simple

[TheJawsusNSexmanShow]

9:42

[TheJawsusNSexmanShow]

9:42

[sullivanseven]

You can also use a handkerchief for erasing :)

[MrSEVAK601]

great video!!thank u so much!!i it' was so hard for me to understand those with absolute value, but now i got it!!!! thank  u very much!!!!

[ElectroMikeBirch]

I was struggling with this concept and found you through a Google search. Thanks for clearing this up for me, I feel much better now!

[Mejiera12]

great video as always.

[CatHouseFat]

THANK YOU

[WaiLoungChan]

THANKS PAT, limits test tomorrow!

[Hallucisquid]

You're the man

[Twolf004]

Just figured I'd let you know. This video helped out a bunch. I like how you break it down step by step, it really helps.

[bcon4136]

you're a hero, thank you

[meow5887]

awesome video. I was so confused about this topic, and now i feel like i'm a genius.. thanx.. clips with more complicated peoblems will be appreciated...

[sebastienthinks]

PERFECT,

thank you!!

[karlkarlkarl1234]

I'm just going to put it out there: Patrick's clips are better than Khanacademy.

There, I said it.

[AmaymonF]

Oh dude, I got it. :D

[AmaymonF]

Limit of (abs(2*x-1)-abs(2*x+1))/x as x approaches zero.

[karlkarlkarl1234]

Does |3 - X| = 3 - X?

[arxaiosthissioths]

this is too FUCKING EASY and you made a video for its solution ....how fucjin stupid!!...!!

[Osiyor]

Morons like you should think before typing... by the way why did you click on the link to watch the video when you find it "too fucking easy"... oh, i know why, because you're a A - Degree Moron. Do us all a favor and think before you type next time... Imbecile!!!

[BaronMorte]

Spider Man? Hell no! Patrick is the freaking Incredible Hulk of math!

[SamSmith29]

absolutely amazing. I've pretty much watched all ur videos. This is really helpful for my Calc I exam tmrw. thanks again!

[Gtownprincess16]

oh my god! I think you just saved me for my calculus final on thursday....my professor is convinced we should have learned this in high school and would not explain how to solve an absolute value to me, even when i asked. My high school teacher must have been slacking because I've never seen this before!! THANK YOU!

[sullivanseven]

You are the spider man of mathematics

[izo1992]

thanks man ... wish if u were personal teacher.. many thnxs

[Lawcheehung]

1:25 middle finger WTH IS THIS

[emcunderground]

@Lawcheehung a piece wise function

[yoshi360360]

"its going to be a shit...ahh stretch"

[TheCoolfez]

@yoshi360360 lol I think he was going to say 'shift" but caught his mistake so he stop in the middle of saying it and it came out sounding like shit

[Zakiller1]

no homo... but i love you! once again you saved the day.