Limit Examples (part 1)

[MrSUAVEtech]

this example is piss easy.. harder questions are difficult

[EkteBoy]

0/0 is undetermined *troll face*

But honestly these vids are really helpful :) Great teach

[dynamo50]

Lol, how many people expected Sal to say the answer was zero in the first part of the problem? I solved the numerator part of the problem and pretty much expected the answer to be zero. Oh do I have long ways to go .__. ....

[namanjaincool12]

best teacher

[DarkKiss92]

you make math really simple, clear and interesting! Thank you very much!:)

[TheLoveformankind]

My question : Is f(x) = y . PLEASE HELP ME KHAN

[mexicanmansam]

@TheLoveformankind Yes, it is (pretty much). f(x) denotes any dependent variable, and is read "function of x"

[TheLoveformankind]

@mexicanmansam  thank uuuuuuuuuuuuuu

[hihohi1231]

Do you guys think I have proplems if im 14 yet i listen to this stuff and get it?

[QtheQuartermasterMan]

@hihohi1231 Same boat as you. No problems, just extreme interest in math.

[hihohi1231]

@QtheQuartermasterMan lol, thats good. But really is this suppost to university math or what?

[QtheQuartermasterMan]

@hihohi1231 Junior/Senior in High School to University

[oOdorieOo]

from now on, I won't even go to lectures at my university, I'll just ask for the list of the topics we're supposed to learn in the semester, and search the videos for them on this channel. :))

[lorenzosan18]

thank you :)

[allen5434]

0/0, point discontinuity. ?/0, undefined.

[JohnathanLeeSprite]

Is that you, Samuel L. Jackson?

[suliemanhs]

watch?v=EhrYQrLBiTQ

[upofftheground]

SO HELPFUL oh my god

[Alarm451]

This guy is very clear, I don't understand how some ppl can't understand this.

[93stormer]

When I arrived in college, my professor automatically assumed that I remembered EVERYTHING from all my past math classes. Sure I could factor and use trig functions, but I don't remember what I don't use. I was lost when we started on limits, until I saw these videos. Khan at least doesn't automatically assume that you remember everything. His style allows you to refresh while still learning a new concept. How ingenious...

[nellajayec]

i love the part when he says" undefined, uuuundeeefinneed" in a low voice. XD 3:45

[monday2471]

i don't get it. how can a function "approach 2" if it already equals 2?

[Eastbay007]

Um...0/0 isn't undefined. It's indeterminate.

[wazed8]

8 people will never be able to learn math in their whole life

[bibbi18118]

he knows how to solve limits but doest know how to use the pen tool

[cristian616]

I pay $8000 in tuition every year but my professors cant teach

[idiotrun1997]

@cristian616 Dude I'm in a similar position! My Professor at Calc teaches it in a really weird way, and I can barely understand him! It's like he makes things supposedly easy hard! But yeah I'm glad I finally found someone who could actually speak English to teach me.

[X4C1M2]

"The limit is -1"

"Oh crap, I lost."

[pseudorealista]

hey, guys I thought most of the people here will be looking forward to take calc. or taking it at this moment but I cant believe that at this level there are basic things not been understood yet. Like 0/0 of course is undef. and 2/1 is 2 my friend. So, he is right. 2 is the answer to this problem it means there's a hole on +2x and the function there doesn't apply.

[devrat4395]

If one gets some number divided by zero (Not 0/0)...Doesn't it mean that the value of the function at that point is undefined?

[baskoffie]

right before 2:50 you say that 2x+1 over x+1 is the same as 2(x+1) over x+1 and then you cancel out the x+1's and that it results into 2. But isn't the bottom part the same as 1(x+1) which will leave you with 2 over 1 after you cancel out the x+1's?

[Mihre2]

@baskoffie 2 over 1 is 2...so you pretty much did what he did...

[yannbane]

Did you just... Divide by zero?

[GODIpraise]

this is not helping at all

[supercalifragilismic]

i understand how it was solve but dont understand what the answer "2" means.

[k1dude]

@supercalifragilismic means that as x get close to -1 the result of the function is 2

[innocentdevil71]

buy a new pen...

or you could borrow my pen.. :P

[TAJ3737]

something is wrong with my tool.

[shreyas1031]

FoCUs..!!!



[93stormer]

I hate math, usually because I can't grasp the concepts as fast as my professors and teachers wanted. I wish I had found out about this site earlier. Khan does a great job of explaining; way better than staring at a textbook for three hours at a time.

[overblast0000]

you should do the slash in 0 for undefined, save some space

[anthrax70]

can there be more than 1 limit?

[dumitrulunic]

use linux

[revengeofbutthead]

LOL at 0:21

i heard you said

"once again my PENIS not working"

[locc408]

thanks

[shakeitbeforeubakeit]

mhmm this tool  lol

[fefafe334]

thanks for mking this as understandable and as easy as possible..

[comptechgamer]

The reason why Khan is so great is because he is related to Genghis Khan lol

[braining1]

I swear that if I had the money I would give a millions computers so just keep going

and thanks

[J03SA]

use MS PAINT! no complications, no hassles (y)

[laneadamj]

Khan Academy is the best!

[PoliticalJohn]

I love you Sal.

[PaulENomeal]

Basically, it looks like limits are a way to deal with exception, from what you've explained so far from the previous video and this one. For example, we can divide by any # except 0, as you showed in your first example.

[Neutrinoghost]

"somethings wrong with my tool"

May I suggest a Urologist?

[jiffy973]

plus or minus infinity right? is the answer to the last one

[synchronium24]

@jiffy973 Sort of: the limit from the left is negative infinity and the limit from the right is positive infinity. However, customarily, it would just be positive infinity because people tend to refer to the graph of the function for x>0

[synchronium24]

@jiffy973 Actually, according to Khanacademy, the limit is undefined since the limits are different on either side. You can see for yourself in his next video on limits, "Limit Examples (part 2)."

[Hackiesacker007]

I like PatrickJMT better, but you guys are ok.

[synchronium24]

@Hackiesacker007 It's just one guy, but I agree that PatrickJMT is better (or at least better at explaining thoroughly).

[spongj3m3]

@Hackiesacker007 why did you need to say that?

[Hackiesacker007]

@spongj3m3 because PatrickJMT helped me pass Calc II.

[ZainulabdeenK]

sir what if the y value had been 0 would the x limit equal 1?

[momeika]

oh god i have a test tomorow and this is like my last resort...this is not how i planned my senior year in HS and we cant even use calculators...and i do get the concept its just that our teacher is really big into labeling and sometime like if we dont label the right things we get points taken of and that really hursts the grade...

[aftershock16509]

khanacademy, thank you so much for these videos. i, out of many people in the classroom, is struggling in calculus, and these videos are a saving grace. it's a complete shame that my school blocks this site, though.

[thejohn95]

@aftershock16509 Wow that's so stupid that they block it.

[synchronium24]

@thejohn95 Damn straight. If they think this is cheating, they're off their fucking rocker. He explains (better than many, many teachers) how to do math and many other subjects. I think they're more concerned with job security than student integrity.

[EpicAthiest]

Wow. 1600+ videos all by yourself.

You're a living legend!

You're not boring like those math teachers in school.

[susanabo25]

this guy saves my life on a daily basis

[xxxXPrisonBreakXxxxx]

In Soviet Russia, Infinity approaches x!

[eleno342]

awesome

[leudne26]

You are amazing,I love your videos.

[samuel1abarza]

I hate my teachers :(

[doublebassrox]

im entering algebra 2 this year will this channel help with some of that? can i submit questions?

[Yvesiscool]

@doublebassrox No you just need Geometry and Algebra. Why would need calc for algebra 2?

[doublebassrox]

@Yvesiscool i meant this whole profile. not the video. are there videos that help with algebra 2? stuff like that. duh how would i use calculus on algebra 2?

[ScorchinBeats]

@MrRelapser for the fucntion of x (2x+2/x+1) substitute x for .999 or whatever the numbers are

[MonaRocks09]

@MrRelapser you could do it on a calculator, you'd see the trend that it gets closer and closer to the number it should be.

[MsGrammarnazi]

You are awesome...show your face!

[timmytankTK]

@MsGrammarnazi Hes been on the news. look him up

[jmike005]

... :|

[Goodyemani19]

Omggg guys he teach soo clear and easy. I wish I had him as my per.

[hoozah17]

@MrRelapser when you're finding a limit, basically you are looking for what the limit equals as you approach the x value. if you are looking for the limit of x as x approaches 5, it would make sense that the limit is 5 jsut by plugging 5 into x and vaoila, but sometimes there's a hole in the graph and it ends up not being that easy making the limit undefined at x = 5 (from a cusp or asymptote maybe), so if you plug in for example 4.9999 and 5.00001 and the values come out really close to 5.

[totopotomoy]

Sal I hate to bother you but you have to do something on Beer's Law...Pleeease!!!!

[tito2541]

off to get a 5

[Tungstenum666]

Ahhh! nothing like a good dose of math to soothe the brain!

[hsktoadftw]

who would pay him if he is non-profit?_below is a dumbass

[TheAbelChavez]

That was good are you a real professor or you just do this for fun? Cuz if its for fun you should get paid

[theULTIMATEanswer42]

HAHA i'm gonna use his site and try to test out of geometry and algebra2 maybe even trig and take pre-clack softmore year (high school)

[mrhnm]

You can I used it and went out of remedial math 0750 (around middle school math) and into intermidiate college algebra.

[kriziapink143]

tnx 4 this =)

[killy0urself]

ah you're so helpful

and your personality is cute :)

[izag1001]

Thanks man helped alot better than my prof!!!!

[nodollarsign]

lol technology gets in the way ;)

[allbout2010]

very helpful

[keitaidenwaKern]

why don't they just say Y instead of f(x)??

I mean isn't it a lot less confusing??

[Ringlev]

It's because the concept of a function - thats f(x) - and an equation - thats Y - is not the same. A function has more complicated uses than an equation. It's not easy to explain here, but there is a difference :)

[MunchVids]

You could say y=f(x) and then use y.

[floopsie666]

Functions are used for more complex things such as program functions.

[GGAlice1]

it was very confusing for me when introduced also, but your not always solving for a y value so using f(x) early on helps the transition when your not solving for a y value (x,y) as a point = ( x, f(x) ) it just means what is the result of x pluged into the function basically function(x) = some value.

hope that helps.

[JESUSISLORDAMEN]

Can you tell me if the playlist for the calculus videos are in order, I want to learn from the very basic but have no idea where to begin? Any idea

[GGAlice1]

well im finishing up my semester of calculus and this is what we started with, now textbook to textbook what you learn is in different orders depending on well what the writers feel is a good order. according to their websites the calculus playlist does follow my last 18 weeks of study. with minor variation that you will get like i said from class to class.

[GTSRBOY]

good old windows computer breaking down

anyway nice tutorial your the man

[leeko518]

@daksh96 No, you're wrong. "f" is simply the name of the fuction. It's commonly used because the word fuction starts with f. f is simply a dummy variable. so "f(x)" is the answer obtained by plugging x into the function f. 'f' means pretty much nothing in the problem, its just a naming device. f(x) and y are synonymous, if you only have one function and you're using the Cartesian plane.

[scottycatman]

@leeko518

99% correct. You just have to remember that z can be a function of x, so you can't say f(x) and y are synonymous. Everything else you said is solid!

[spectralofficial]

@leeko518 when would you NOT use a Cartesian plane?

[StuntChickenAu]

@spectralofficial When you're using complex numbers, where its called an "argand diagram" :)

[lolitaforever333333]

thx alot

[kokojohoko]

f is a function, not an axis

[drfan2004]

what does 'f' mean? is it the y axis?

[freedomgundam1993]

f does not have a mean, your trying to say f(x), you would say that as "f at x" ,and no it is not the y axis

[Aashish7K1]

Good tutorial,man!

[patilnikh]

Thanks again Salman!

[Helpbot]

I love you dude

[cremions]

good man,,,i liked the way expalain by graph....nice ,,,n thanks sal..

[abunigel13]

it all makes sense!!!

[farzero]

thanks a bunch man, these videos are amazing. I just got out of class and I've been watching these videos for the past hour, very helpful and entertaining.

[dominicfhk]

million thanks!!!

[ralliplane]

Thanksss!!! You help me a lot!!!! I Love math when understand jajaja

[dankf08]

"I think my computer just froze"

[ETERNALinstants]

Even your pc knows this is hard D:

[marcusjhung]

Computer Melt Down while running microsoft paint FTW

[mrhnm]

What is FTW?

[Runningscared4ever]

For The Win!!!

[thechessgeek]

I LOVE  MATHH

[jessecax]

@thechessgeek thats stupid



[remusomega]

@thechessgeek

I LOVE METH!!!

[liverpoolmatt87]

@remusomega you must  be a "high" achiever :P

[slashgashshorty]

@thechessgeek i used to think that before college man



[slapointe31]

Wow, thanks a lot. I'm back in school and math are so far in my mind. Looking at your videos help me a lot for understanding. My teacher actually get through this too fast for me. Thanks again. (excuse my english but I'm a french speaker)

[MsGrammarnazi]

You have a really great teaching voice.

Oh! I like the lime green pen.

Dana

[nietzsco]

8:26- Something's wrong with your tool!? I'd go to the doctor and get that checked out.

Sorry, I'll get my coat.

P.S. You are a legend for creating these videos

[hirohamaman]

i love math :)

[patronpatron1991]

@hirohamaman bende matematigi seviyorum <3

[MidgetPhilosopher]

Incorrect, BUT lets say f(x)=.ooooo1/x

you can calculate the lim as x->0

In which case, 0 is the limit as X approaches 0.

[clarinetmeister]

For f(x) = 1/x, the limit as x approaches 0 is negative infinity from the left side and positive infinity from the right side.

[Wuzzi55]

hahaha, froze by using microsoft paint? *LOL* Thanks for the teach though. You're really a nice teacher.

[sherilyn222]

I got a question. If the limit of X -> 3, would X = 3?

[Manu9324]

0/0, infinity.0, constant/0

all r inderminant forms

[kimpoi00]

hahaha.. curse you evil pen!!!! btw.. i really like his presentation.. this video really helped me.. our topic tom is limits..

[Psyzoid]

his pen malfunctions.

[Phosphoer]

Just got back from math class, watched this, and now I understand limits :p

Great work :)

[Ashmaer]

lim |x-5|-|x+1|/x-2

x->2

so is this indeterminent?

or can you solve this?? but im confused because of the absolute value, how can u possibly get rid of them?

[xxSaraixx]

I am taking calculus in college, but i was tought that when the answer is 0/0= indetermined, and that when a number/0 = undefined.....

[youlovethatonebarry]

lim x^2 − 5x + 2.

x->4

can anyone help me solve this please?

[AkiraVshT]

I think it's -2.

If you try substituting x in the x^2-5x+2 with 4 or numbers close to 4, you get -2 or numbers close to -2. I THINK, but I'm not the best limits-person. Ask Sal ;)

[Beefstew2011]

The function is continuous at all places, so you can just plug it in. -2

[jrendoso]

yes dude, the answer is -2, just replace 4 where the x is and do the multilication

16 - 20 + 2 = -2

[xXfrissionXx]

omg I <3 U!!!!!! HAHA thanks so much for these videos, it's starting to make sense

[youngnuts202]

This is amazing! You can teach so much better than my math teacher lol. If you could keep these up, that would be great!

Just a side note, instead of writing out the word "undefined", just use the symbol. (the circle with the line through it) and just explain what it means in any future video/s. It should save you time :)

[adda180188]

oooh ur so patient. and i think u have a very soothing voice.

thanx!!!!

[adda180188]

oooh ur so patient. and i think u have a very soothing voice.

thanx!!!!

[thisaintminhma]

ahh sorry i was giving you a 5/5 but my cursor moved to 4 im sorry! but you are great!

[32docholiday]

HAHAH - ur a funny guy - compter froze , really appreciate ur videos,

*start easy then get into harder problems - like the limit of a sin, tan or cos function(if u can). thanks a lot!

[citrizz]

perhaps use ms paint to record your gestures ?