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

[Saronaist]

Nadia is lucky :D

[DaveGrennan]

Just wanted to say a big hearty thanks for these presentations. Really excellent. Big thumbs up!!

[dacat]

An easier way of doing it, Differentiate the top and the bottom, (2z +2)/(4z^3) = 6/32 when z=2

[martystreets]

i love khan greatest teacher alive. real talk and ur funny too

[mken83]

Shouldn't the first problem work out to 6/32 rather than 6/12?

[gluegunassault2010]

@mken83 it is check description

[0verlordQc]

I had the exact same problem as the fisrt one in a homework, and I did the same mistake xD

[ranvideogamer]

My Alg2 teacher used to teach this to us XD, it wasnt in our curriculum necessarily and this is one of the things tht got me a D for the year.I mean she saved this stuff until the end of the year but still it was annoying and was like pre-cal stuff

[iLiyadokov]

I'm so conditioned..

Like a dog.

AHAHAHAHHAAHHAHAHAHAHHA

[TheLoveformankind]

OMG, I AM IN LOVE WITH NADIA !!!!

[brco2003]

Nadia is o famous, lol!

Love Sal and KhanAcademy!

[rhymenorreasonable]

Can someone explain how he simplified 4/(root1)+1 =4/2? 

[ShadowPhoenix951]

@rhymenorreasonable Sure. The square root of 1 is equal to 1, so, in the denominator, you end up with 1 + 1. Which is equivalent to 2. So, the numerator remains a constant 4, and the denominator adds up to 2. So you end up with 4/2. Does that help any?

[rhymenorreasonable]

@ShadowPhoenix951 Yeah it does, thanks. Sorry, My math skills have been lagging. That was a pretty dumb question.

[amaclellan3]

middy tmm too many drinks this weekend, you saved my ass, crammin like a boss!

[cheatsisbrown]

@HYD1505 That's a trig identity - double angle formula

[curlymike]

So after researching "alcohol dance" I typed "brain malfunction" in YouTube search box, and that's how I ended up here.

[HYD1505]

I don't get how you got sin2x= 2 sinx cosx?????

[KurdRaw]

what is the program he uses

[TwistedLemniscate]

@KurdRaw smoothdraw3

[LoganBlackP]

This is soooo much easier now. thank you sooooo much

[AnotherBrownKid]

im soo confused in this video!

[JointCracky]

damn.. how can it be that really almost everyone hates his teacher at school , because he can't explain! i know i am one of those.

Still a great teacher once , who helped me a lot , but now i'm using internet to learn MATH! it's supposed to be the easiest subject...! why do i go to school again? for knowledge? yea....sure don't buy it.. :P

Thank you a lot ,sir! you're our hero! ^^

[shalacktan]

why is it 8 times 4 and not plus, i dont get!!

[Hikayuhuy]

@shalacktan because they were mutliplying in the previous verse . when you have a parenthesis next to each other , it implies they are multiplying each other . a plus , obvious came out of nowhere , messed up the denominator .

i love these videos . im taking a challenge test to skip ahead , forget taking classes . i just need a couple months , these videos and im good .

[devrat4395]

1/Infinity =0 so aren't you multiplying and dividing by zero in the (X^2+4X-1)^1/2 -X ? That will be like 4*0 =5*0 So, 4=5...That doesn't make sense... Can you clarify this? Or is it because X never really reaches Infinity so it isn't exactly 0?

[JayantKumarZ]

chu made a mistake :3

how cuute ;D

[nidihudi]

Just because of you khan academy

I am always 3 steps ahead of my entire class

THANKS A LOT !!

[navoditc]

I am lovin' it.

[3croN]

brain hurts .....

[dennissumeeloonn]

I'm so condition like a DOG hahah

[MrNeverataner]

"modular arithmetic" please.... @khanacademy

[Silentsam7532]

I have been watching these videos to help me after Calc 1 class. I don't know how I got this far without really understanding why we multiply by the conjugate. It makes so much sense now.

[hammd123]

Thanks to Nadia as well. Its because of you Nadia that the whole world or i should say humanity has started learning the world most complex mathematical science. A well known sayings "BEHIND EVERY SUCCESSFUL MAN THERE IS A WOMAN". May God bless you and all the team members of Khan academy.

[born4computer]

Hey, I don't want to be a jerk but 2:25 you don't add; you multiply.

[0xstrx0]

@born4computer

If you read the description...

[mau5ForLife]

I wonder if he reads these comments and realises how much of a legend he is :-/

[Magik0722]

Hah i memorized the trig identities the same way

[Cheezmago]

I actually applauded you.

[BattenburgBoy]

I wish you were my cousin....

[narcomanel]

lol, one half XD

[kungman190]

why did he write 1/x/ 1/x why don't he just write x/x???

[JanWey91]

@kungman190 x/x woudnt work as that would multiply x-squared by x not "delete it out"

[kungman190]

what's the highest degree term mean?? any1

[vanr9814]

You are a better teacher than my prof XD

[GoldenChildBH]

Sucks that my teacher gives us questions 29x harder than these simple ones. But this video kind of reinforced the basic steps of solving these things. Thanks.

[usabaseball8]

stop using the weird symbols? mkay? thx(i mean like the triangle and the whatever that is at the begining... or maybe do a vid on them

[denni0302]

@usabaseball8 'stop using weird symbols' those are official mathematical symbols....i havent watched the video yet, but im guessing by the triangle you mean the delta symbol, which means the difference. ie delta x = x(a) - x(b). As for the very beginning (lim z > 2) watch khans introduction to limits vid.

[usabaseball8]

@denni0302 i meant he needs to say what they mean... but ik wat they mean now ... just in the future...

[BogdanStanciuMusic]

thank you, i am finally understanding this "things". you are helping me graduate, you are helping me more than the teachers at my college . you are a kind man. can't thank you enough. im sure now i can pass my exams, finish college and start the life that i always wanted

[sozinification]

@BogdanStanciuMusic - dats so cute.wish u the best.

[92sgr]

i wish i had a cousin cousin like ya cousin 'nadia'

[pithikoulis]

what about logarithms? i have this "find the limit of ln(x+x^3) / ln(x^2+x^4)  as x approaches infinity". what should I do with the ln? :S

[Almaasak]

I wish I could be ur cousin!!!

[intnull]

At 9:50 what you're saying is incorrect, it should be

sqrt(1/x^2 * a) = abs(1/x) * sqrt(a).

However since you're looking for the limit as x goes to infinity what you wrote down is true. Still, it could be confusing since you didn't mention, that x>0 in this case.

[jbeddiejb]

Even though I already knew about the conjugate use in these example I couldn't find a way to use it for this EXACT homework question I had, thankfully example No. 2 helped me out and allowed me to cancel out the issue in the problem. Thank you,sir! You help me once again :D!

[kurrizzle]

I FEEL SO SMART NAO!

I THANK THEE!

[spaaceful]

brilliant!

[mroglow]

Good dude great vids!

Got one question shoudnt u re wright it like this (1 problem) where it is

x^2+2x-8= (x+2)(x-4) ? you wrote it (x-2)(x+4) witch would make it x^2-2x-8 or am i wrong?

[jbeddiejb]

@mroglow You are wrong, (x-2)(x+4) = x^2+2x-8 because -2 and +4 will make +2 :P

[mroglow]

@jbeddiejb

A few times every year i have days where George W Bush seems smart compared to me, that was one of those days:P

[jbeddiejb]

@mroglow Nah, no one could be lower than him.

[silvenflame]

i smell fail. =D

great videos anyways

[Michalbasavraham]

That's the same Nadya that needed help in 6th grade and set this whole thing in motion, no? And she's taking calc now... wow!

[gvsfgdf]

L'Hopital's rule could have saves you alot of time... -__-

[10mrRight10]

hey teacher...this was very awesome..u arouse my interest on limits (and calculus) more!!thanks a lot..

[Michalbasavraham]

@10mrRight10 He's not technically a teacher which just goes to prove that "teacher training" is nothing for producing good teachers.

[10mrRight10]

@Michalbasavraham agree!!

[MonaRocks09]

yayyy reppin desis well Mr. Khan :)

[no0000ob]

if the expression inside the square root for the second problem...

if it had a higher power like....

x^3 + x^2 etc...

if that was the situation... would that now be the highest power?

like... would we not multiply by 1/x now?

[ballsoffury4]

Can someone explain to me why cos2x=1 in the last part of the video?

[JohnNumberThree]

@ballsoffury4 If you graph the function y=cos(x) on a coordinate graph, you'll notice that when x=0, y, or cos(x), is equal to 1. So, as x approaches 0, y, or cos(x), approaches 1. The same goes for cos(2x). The only difference is that the graph of cos(2x) has a shorter wavelength ( I believe). Hope that helps :-)

[ballsoffury4]

@JohnNumberThree

Yes it does, thank you very much =)

[batistawis]

@ballsoffury4

x=0 so 2x also = 0 and cos0 =1

[Millsie18]

I must thank you so much! You've helped me out tonnes!!

[ccinbrainsurgery]

I have a question on the second problem .. when you end up with 4 / (sqrtof 1 + 1)

shouldn't the sq root of 1 be +1 or -1. So the answer is either 4/-1+1 or 4/1+1 .. thats infinity or 2. Is this correct ?

Great videos btw. I am a fan of your teaching.

[wwf101]

why does cos2x equal one?

[azntlx]

dude, i love the way you teach. you also have such a funny sense of humor. lmao.

[Oohviyakiruki]

at 03:49 onwards..

.i don't understand ..

when u substitute the Z with 2...how do u get (Z^2 + 4) (Z^2 +2) = ( 8 + 4) = 12, isn't it should be (8 X 4)=32.

could someone give me a hand

[SuperhumanChichi]

@Oohviyakiruki

Look at the caption he made - he corrected himself a while back.

[Oohviyakiruki]

@SuperhumanChichi

10q v m

[prettynathie]

this videos tricky

[MrJMOwens]

Any videos on limits of trig functions?

[montrealexpress]

why only the principal root in the last step?

[sharkbait2712]

At 8:08, I'm not understanding we're dividing 1/x / 1/x. Can anyone break that down more? Thanks.

[partygreens1]

@sharkbait2712 -i think that's actually kind of manipulation we are applying. U may not just divide it by 1/x but take x common out in the numerator and denominator.

[GetMeThere1]

nice ones!

[schmolck]

This is fun!

[YoungYemeni]

Khan is the top professor...mad respect!!!!!!

[onnis1]

Khan...you just too good...these goons who appear to be trying to correct you...have tried to be as good as you but in vain,you are here to teach us,ur style is extra ordinary!!! we appreciate...

[edmun09]

sal, you were born to teach :) thank you so much for all the math videos :D

[andreiduffy]

MORE

[V3niX]

just press ctrl+Z.. u don't need to click edit-undo evry time..

[timtu22]

Maybe he has gotten himself into one of those comfortable positions where the keyboard is too far away so you try and do everything with a mouse.

[lolitaforever333333]

that was excellant

[nicolaus1990]

If you can simplify a function to get its limit, couldnt you simplify a function to get f(z)=3/16 (first example, where he got it wrong and got 1/2)

belive me I understand limits! but I cant pass that thought.. for me its like a contradiction.. please someone explain!

[thinker6236]

man how the heck did isac newton came up with these stuff. it must of driven him insane just come up with it before understanding it.

[thejugglenaut91]

the things he came up with were infinitely more insane this limits haha. I can't even comprehend.

[thinker6236]

i know, im talking about i calculus in general. anyways, Only if he was alive today imagin what he could do.

[svenkatesan]

The second problem can be solved more easily.

The main problem is the square root , to remove it we can do a technique known as completing the square x^2+4x+1 can be written as (x+2)^2-3.

As when x approaches a large number we can neglect three.the equation reduces to (square root of (x+2)^2)-x which becomes x+2-x=2.

[ZnBangash]

@svenkatesan

Could you explain why you neglected 3?

[klezaz]

'I'm so conditioned, like a dog' cha cha :D

[Gourcuff2008]

04:09 it's 4 . 8 not 4 + 8

[pokaymahn]

no shit, he says that in the description

[jianzzz88]

why - him? he stating the truth that it is 4x8 instead of 4+8... ?

[niposs]

I can't understand from 02:00 to 02:50 ...how do u get them?

[misterblackdark]

You have to know the rules :

a² - b² = (a-b)(a+b)

a^4 - b^4 =

(a²)² - (b²)²

= (a²-b²)(a²+b²)

If you're talking about the upper part(numerator), that's factoring quadratic equations. You might find it in his Algebra playlist.

[alitou001]

@niposs check a lecture about factoring.

[sallamatt]

U make it so easy, thanks.

ps. I wish I was your cousin Nadia! ;)

[gobberpooper]

1) It makes it seem more like a classroom where he's drawing on the board instead of those random boring videos where the pictures just pop-up. No thought process

2) Does it fucking matter? I had a B- in Chemistry and after watching just one or two videos a day, I got an A+ for my second semester.

[chuubear]

loves it, thank you. :) your videos are the best ^^

[jm5vh7]

you rock; I learn more from your videos than what I learn from the prof

[esponjabbpr]

TRUE DAT!

[JLarry09]

thank you thankyou, my calc teacher doesn't speak english well, and your videos helped me alot. please continue to post more vids.

[themanso08]

ok at 5:56 and the whole problem im lose

[archeafable]

Difference of squares can also be done by FOIL, but the middle term would just be 0. So we simply do the shortcut.

[lseateal]

how come we dont do FOIL when we multiply the numerator of the conjugate?

[dainese01]

because we can apply the difference of two squares rule.

the a part is squared, and the srqrt cancel.

and the b part (x) is squared.

quicker and easier.

you can still FOIL if you wanted... but learn the rule, its better to know

[mklvebu]

You're an outstanding instructor!

[TookyTooky21]

I don't exactly understand why you are dividing by (1 / x ) at 8:06 for the second problem. Can you please explain it to me....?

[ubercute1sf]

if he devides both the numerator and denominator by x the value stays the same. he's just trying to simplify the equation a bit. i hopethat answers your question

[Prolocater]

thanks a lot now I can solve that limit problem

[Prolocater]

hello can you help me factor this

x^4 - 3x^2 -4

[obsdj]

It's very easy.

Set x^2 = h (or any letter you want, really)

Now your equation becomes: h^2-3h-4

Which is easily factorised to:

(h-4)(h+1)

You then replace h with x^2 and you get

(x^2-4)(x^2+1)

[guest2031]

(x^2 - 4)(x^2 + 1)

[tropicalmist999]

Khan do you do LSAT logic?

[pokemario64]

too much patience, go faster

[Giovanni2666]

Please Tell your cousin Nadja not to give you problems like this anymore.

[libbeingcool]

noo we need more problems like this it helps us prepare for the test

[Giovanni2666]

I know, I know. I was kidding.

[babycracka13]

you make my heart super happy

[1a1a2a3a]

The second one is messed up, sooooo hard!

[libbeingcool]

I agree

[Gaussdxdydz]

Hello there. Em, I propose a shortcut to find the limits. Instead of factorising like you do, we could maybe treat the given function as f(x)/ g(x), and differentiate each separately, and then plug in the limiting value. Eg in example 1, we differentiate while considering numerator and denominator as two separate functions, and then place them back, we get (2z+2)/(4zcube-16), and when we plug in z=2 we get the limit. Is that correct? What do you think about it?

[Cagebreaker21]

That's L'hospitals Rule and it will only apply when lim x-> a f(a) = g(a) = 0 or g(a) = + or - infinity.

P.s the derivative of x^4 - 16 is just 4x^3.

[jeanotho]

thanks alot for the uploads !!!

[khanacademy]

You are both correct. My brain malfunctioned. The correct answer is 3/16. Thanks for catching that.

[Uroshnor]

At the four minute mark, 2 squared plus four is multiplied by 2 plus 2, not added. So, it would be six over 32. So, the final answer would be 3/16. Correct me if I'm wrong.

[SchizoKnight12]

u got the first limit wrong. lim z-->2 (z^2+2z-8)/(z^4-16)= 3/16. check the denominator. you added 8 and 4 when u should have multiplied.