Limit Examples (part3)

[Lucifar1990]

"I'll do this fast so I can confuse you" haha love these vids. thanks so much.

[digimonkeisari]

my overnight cramming has never been so effective

[moka22051]

i thot khanacademy would help :(

[damthatriver09]

@moka22051 Not if you don't put in your effort.

[anayala]

finally someone who can explain well

[w00tw00t898]

@3:54 Let's say what is... penis not working :/

[Goklet]

As you go to the infinity... AND BEYOND!

[avemunsayac]

I'm 15 years old and you're saving my life!

[download333]

@1:02, Best calculus teacher ever

[drmo92]

I dont get your very last example. How can +x above the divide line be irellevant when its an infinitevly LARGE number?

[BigBlackNlGGA]

@drmo92

Because that infinitely large number will be infinitely larger when you square it and multiply it by 3, so the ratio will still be 3/4. more like 3.0000000000000000infinity0000­000000000000001/4

[SWATsqad]

@drmo92 because it's just an x ? the 4x² would more than cancel out the x above ( relating to 3x² ).

[TheLoveformankind]

confusing

[TheGreatBrendon]

What did students do before khan academy? D=

[Sasha7amad]

Am so glad ur videos get over a 100000 views! Just months ago they were much less, and hopefully in a few they''d get over a 1000000

[tanvirul23]

@arnoldbertil Maybe he needs to make a video on grammar and spelling, you would learn a lot from that video. I mean come on, nobelprice????

[MilitaryMan006]

Can I put sad face in an exam?

[maxismydog101]

Pshhh he doesnt need to go to school, he just decided to get a PhD in life

[chiboy3000]

Thanks! This will help a lot in my AP Calculus AB class. You made me understand this subject even more. =) With your help, I will make it to AP Calculus BC and AP Statistics next year as a senior! =D

[Xboxfanftw]

Thanks sal for posting these videos. I'm in Calc AB AP right now and i have a test tommarow on limits. After watching 3 videos i've learned more than watching my teacher teach limits. I just want to say keep up the good work and make more videos. Esp on Math cause we all know how important math is. Damn I sound like a total nerd lol

[KongXJ168]

@arnoldbertil nobel prize can't u spell?

[atladventureboys]

@KongXJ168 = They haven't gotten to Khan English yet.

[Br3nD0g]

YES MORE LIMITS!!!! GET IN!!!!

[MixesAndStuff]

@AcutePorphyria hahahahaha

[cifier]

Question: Before time stamp 3:44...

One limit is set by the factor ( x - 3 ).

Would another limit be set at -3 for the factor ( x + 3) in the denominator?

[elmerjal]

its midnight right now, I have a calc final at 11am. pulling an all nighter going over all your videos.

[eunicellular10]

@elmerjal same hahahaah

[allain14]

do ones with radicals... I just can't get my head wrapped around those squareroots...

[tyrenebanks72]

@arnoldbertil

I know this comment is a year old but i love it lol. Sal is the reason why I got an A in a math course I had taken a little over a year ago. I'm back and using these pre-cal videos to preview before I officially take my pre-cal this fall.

[dahelgster]

"Lets explore that!"

Pure awesome. Thanks for the help.

[CCHERM]

No, because when you deal with larger and larger numbers like trillions and so on, those lower degree parts become less and less significant, making it approach 3/4. In other words, the larger the number, the closer it gets to 3/4, making that the answer.

[narcomanel]

Well, it is 3/4 if you ignore those small numbers, but they still exist, and it isn't exactly 3/4, right?

[DarthHater100]

I have a question I was hoping somebody could answer. On my graphing applet, when I put in y=x^2+6x+9/(x^2-9) or y=(x-3)(x-3)/(x-3)(x+3) or just the reduced (x-3)/(x+3) I get 3 different graphs, although these are all the same, just different forms. What's the deal.

[KoreaXFan]

SO I guess THIS is what my teacher was trying to teach me....sigh,

[tIs4gatorbait]

"lets do some more limit examples!" one the best parts about sal is his contagious enthusiasm.

[Eltron25]

What i'm not getting at all is when he simplifies the F(x) of the first problem like

"x²+x-2/x-1" and he says that it's the same to put: "(x-1)(x+2)/x-1"

I know that if you make the math you'll get the same.. but what i don't understand is how to make that by my own :/

[aambris010]

@Eltron25

When given a polynomial, always see if it will factor down.

1) Make sure the equation igoes from highest power to lowest power, listing the constant last. (x^2+x-2) is already ordered since the highest power (2 from x^2) comes before the lowest power (1 from x) and finally the constant (2) at the end.

2) Now, looking at (x^2+x-2) what will add/subtract to = 1 (the coefficient of x) and multiply to = -2 (the constant). Well, 2 and -1 will. 2-1=1 and 2 x -1=-2

Thus (x+2)(x-1)/x-1

[Killuminatismd]

this guy is a genius :)

[gavin32]

which video helps with learning how to factor things like x^2+x-1 ?

[wafflecraft]

@gavin32 The overall algebra section, however if you have trouble factoring things like x^2+x-1 I suggest you don't start learning things like limits quite yet

[bothar54]

can you use L'Hopitals Rule here now??

[otakughost]

@bothar54 According to a reply a user made a year ago and that Sal answered to, yes, you could. But according to the order of his videos, Sal hadn't taught derivatives yet, so he assumed the students didn't know it. And therefore didn't use it.

[chris1990re]

if you're looking for an easy way to graph functions, multiple graphic calculators can be found online, can't link to one though.

[nutella871]

@AcutePorphyria I don't appreciate your incorrect usage of the contraction "you're."

[Blueknightex]

@arnoldbertil Frank Zappa?

[Thiessu]

I'm in grade 11 and just learned, from you, almost everything I need for Grade 12 haha. Also thanks to the guy in the uploader comments for mentioning L'Hopital's rule! He actually has a video on it and I just learned that, came back to this video and did both questions in ten seconds! :D

[bmdmarie504]

love the sad zero! hah

[leudne26]

You are GREAT!!!!!! I can't believe I am not bored with calculus :) .Good Job!

[DariaDianna]

Your examples are so simple I can do them in my head. Why not enlighten or rather show me how to do some challenging infinite limits.. that would be alot more useful

[mephatboi]

@DariaDianna

watch: Limit Examples w/ brain malfunction on first prob (part 4),

watch?v=xjkSE9cPqzo&feature=ch­annel

[Sonjuro197]

I feel like I'm watching Dora the explorer when I watch this. When he's asking if theres anything to do at about 1:12, I'm yelling FACTOR FACTOR!!!

[KirbehsBizzatch]

I like the little frowny face.

[MsGrammarnazi]

Show your face!

[heyyodoug]

@MsGrammarnazi don't you understand that he is different from others in deciding to let his voice guide the viewer as a voice in your head

[MsGrammarnazi]

@heyyodoug

You are so wise, Doug. SO WISE!

[JohnnyCagePro]

what's the limit as X approaches ... INFINITY!

[ShadTan24]

Can the limit be a negative whole number?

[Kurtlane]

So what is the answer in the first problem: 0/0 or 0?

Answer to f(x) = (x2-6x+9)/(x2+9) at x=3 is 0/0 = undefined

But answer to lim (x->3) f(x) is 0.

Similarly in the second problem:

Answer to f(x) = (x2+x-2)/(x-1) at x=1 is 0/0 = undefined

But answer to lim (x->1) f(x) is 3.

Just wanted to make it clear.

[01whussain]

your amazing!! thankz sal, ur a real hero!!

[baudiirocz]

I wish my calculus professor had explained limits this clearly.

[jtel]

Thanks as always!

[silentperson233]

@ the beginning

THAT'S THE SPIRIT! :)

great tone

[BlueFool29]

this video was posted on my bday lol 3 years ago

[Luckyxseven]

Straightshotz ima teabag u, wasteman how did u no my math mark. I donated 3000$ to khan academy.

[Luckyxseven]

Ur great :)

[kriziapink143]

...wenkz

[idster7]

why couldn't the answer for the second to last problem be one over positive infinity rather than zero?

[iMNice99163]

Again dude, your a saint (the superbowl winning kind)

[ZnBangash]

Lots of people would be jealous of you, Sal. I am 100% sure. ^^

[janaoo4]

An easier way to figure out what one of the factors is is to take what x is approaching (x->1) and then put that as one of your factors with the opposite sign. (x->1) ---- (x-1)(x+2). This almost always works if not always. I've never run into a problem with it.

[aparrotslife]

Sal, you are amazing!!! Thank you very much for making calculus fun! You have given me one more reason to love math. Thanks for your invaluable videos. You're my hero...:)

[MrFlamingoo1]

Sal, I cannot thank you enough!

I just wish I had watched this video before I missed all the limit questions on my precalc final this morning! I'll be sure to ace my upcoming limits test.

Thank you, thank you, thank you!

[lolitaforever333333]

thx a lot

[mensa180]

Thanks man, I'm taking AP calculus next year in high school and figured it couldn't hurt to learn some stuff before hand.

[ILockItDown]

i know the nobel prize, not the nobelprice lol

[CobHateCrew93]

You are truley awesome.I finally understood limits.

[Eggsworth12]

this is so interesting. i am taking calculus next semester and these introductions are really helping to ease my nerves about this new type of math :)

[ILockItDown]

wtf is a nobelprice

[tomnsteve]

you've got quite the little crush

[javib282]

YOU ARE A GOD AMONGST MEN! lol thank you so much Mr Khan.. you rock.. i live in miami and would travel to whereever you are just to take your class.. ive learned more in the past 30 min than i have all semester.. YOUR ROCK.. Saul for President!

[jceja24]

Sal for president ...

[libbern]

When I sat at the university today I got so damn depressed because I could not figure out how a function that is undefined at one point suddenly becomes "defined"... One gotta understand the basics. But now I understand that when you simplify it you actually get the function for all (or most) other input values than the undefined one. Still kinda confusing though, but you did help me a lot:) Thanks

[absterz]

Hey sal, isn't this concept similar to the horizontal asymptotes of rational functions? if so, how can we think about it in this way?

[dual85]

Thank you. I appreciate this! Complimenting my textbook.

[hermangt89]

thank you dude

[Artofoov]

Humm part 2 doesn't seem to load for me. Part 1 and 3 is fine though.

[jhonma1]

Khan, Thanks for explanation

[woodenjaw]

I plugged the last problem at 9:21 into my calculator and i didn't get an error for 3/4

[Budisawsome]

you're not suppose too because the expression is in determinate form.

[megaelliott]

Yes, I substituted 10^100 as x and the answer came to exactly 3/4 because x is so large.

[Endivisual]

:D thank u you've helped A LOT!

[libbeingcool]

the infinity ones are too confusing. i dont know why i dont understand them

[Sproge]

You're wrong.

[XOJinny]

one of the answers is wrong.

lim as x approaches infinity on 1/x^2 isn't infinity, it actually doesn't exist.

[Lolly2810]

This may seem a stupid question but I just want to be able to completely understand these. How do u find the right numbers to divide against when the limit is 0 over 0

[IraqiGladiator]

you could have used the L'Hospital's rule for all of those problems...and u would still get the same answers

[khanacademy]

You're correct. I'm assuming, however, that the viewer hasn't been exposed to derivatives yet.

[arch571332]

Your a better teacher than most 'teachers' in colleges and universities. Their explanations are often symantic that the student end up teaching themselves out of the book or from each other.

[Sonjuro197]

@khanacademy Fucking owned btw. Khan has power over the IraqiGladiator.

[luismariano2009]

@khanacademy and it's l'hopital... jeje

[carlangasnalgon]

@IraqiGladiator shut up you engineer

[exfb64]

@IraqiGladiator stfu you anal bead

[IraqiGladiator]

@exfb64

wat the hell is that for u piece of filth? grow up u illiterate piece of crap..the country is already full of dumb people like u so try not to speak so often so u wont worsen the image of the US

[grimwallace]

KAAAAAAAAAHHHHHHHHHHHHNNNNNNNN­NNN!!!!!

Great videos.

[1a1a2a3a]

thanks!!!!!!! :) :) :)

[Caballorider]

Wait, in the case of (x^2+3)/x^3, x^2 is always >=0, then x^2+3 should also always be >=3, so how can the limit is 0?

[miamimanni]

Perhaps trying it a different way will help you understand. Divide everything by x^3.

You get 1/x+3/x^3. As the x's go to infinity you can see how the whole thing becomes 0.

[cb4allstar2]

so is the limit of the (x^2+3)/x^3.. equal 0?

[Ashmaer]

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

x->2

would that be undefined?

or how can you possibly get rid or the absolute value?

[hopelove101]

Thank you very much!!! you saved my life

[clerlic]

A-mazing!

[jokumusic]

I think I missed something here...

lim as x->1 of x+2

when you say that the limit is 3 doesn't that only work when you're approaching 1 from the negative side? What about when approachine 1 from the positive side?

[khanacademy]

When x=1.1, x+2=3.1

When x=1.01, x+2=3.01

When x=1.001, x+2=3.001

So when x approaches 1 from the positive side, x+2 approaches 3

[jokumusic]

I get it now. Thanks for clarifying that for me so quickly. Just in case you haven't heard it enough already, you're the best!

[beckyp4win]

hahahaha the sad face zero. cracks me up. thank you for being amazing.

[illusion422]

Good video.

I like that you mention why you can cancel out the (x-3) because x tends to 3 but will never be equal to 3.

Comparing it to the same function without the limit then you would have to give a restriction of x is different then 3 to be able to cancel out the (x-3)

[maylien]

Nice! I'll be sharing these with my students.

[dusk440]

Thank you very much, helped me a lot :)

[jmingus]

Excellent tutorial, informative examples--- THANKS!!!

[Isramirez20]

Thank you