More Limits

[FornicateThySofa]

i found this to be way more than vaguely useful.

[chuchiemaaane]

I need help solving 1/(x-1)

[MrEvanCarey]

is there a video on limits of trigonometric functions?

[whoasarawhoa]

I LOVE YOU. Seriously, you're a lifesaver.

[MilitaryMan006]

at the bottom right it says 'Artist: One Playing at The Ivy, Sydney' LOL

[stateofeuphoria12]

When sal is doing the limit of X-2lxl/lxl from the negative side why is it x-2(-x)/-x as instead of -x-2(-x)/-x

[Skelymage]

@stateofeuphoria12 the |x| is absolute, so that is what will be turned negative. the x-2 part is not part of the absolute value.

[selvmordspilot]

i'm lovin' this. I skipped calculus class today, and ended up watching it on youtube instead :)

[SugarRush694]

I'm confused, I thought the absolute value was the distance away from 0? And that it could never be negative...

[werdo21]

@SugarRush694

Yes, but if x < 0, |x| = -x (two minuses cancel each other)

[sin7wu]

can you help me. I don't understand how to do this problem.

The limit is "x" approaching 0 as the (Square root of 3+X) Minus the Square root of 3 all divided by X.

I'm not doing something right no matter how many times I rationalize I can't get the right answer in the book. PLEASE HELP.

[sin7wu]

@sin7wu never mind i got it. forgot to simplify.

[inmotion86]

Another dirty secret? Use an online graphing calculator and then analyze the visual graph (of course assuming you can read a graph well).

[SteDeRaver]

Can anyone help me here? I am having terrible difficulties dealing with Tan and Cos and other things in these questions and Sal doesn't seem to cover it.

E.g: x/sin4x+sin2x

I would REALLY appreciate any help, thanks.

[SteDeRaver]

Can anyone help me here? I am having terrible difficulties dealing with Tan and Cos in these questions and Sal doesn't seem to cover it.

E.g: x/sin4x+sin2x

I would REALLY appreciate any help, thanks.

[DrGreenEyedGiant]

I am extremely surprised at how much faster Sal teaches us math than that of my school. My name is Chanceus Moore, I am 13 years old, and I am studying calculus.

[sepia2008]

Nice:) you can also use the L'Hopital rule for second example

[flyingbeagles]

americas next top model?

:P

[narcomanel]

squeeeeze theorem.

[Aguy666]

Wait... I'm confused at around 5 minutes... when approaching from the left, how come x is left positive but the absolute values of the x's are negative? You get the same answer, but I feel like it should be done the other way around....

[abcsmedotcom]

Just wanted to give back. When you press and hold ctrl, then press Z, on the keyboard, you initiate the undo function. Apple has a similar one. It'll make things faster!

[urumqilik]

anyone would be kind enough to enlighten me as to why we can not use L`Hospitals rule to solve these limit problems??? this is very confusing and it would have been much easier using L hospitals rule anyone?

[111000may]

you are the best teacher i've ever had Sal!!

[MarvelsofaLifetime]

Wow, those were some meaty Limit problems. Solving these kinds of problems analytically is all about practice, but I’d take Sal’s suggestion, when these Limit problems start to become too advance to solve analytically with intuitive reconciliation then you should just substitute values extremely close to the value which “x” is approaching.

[alldae09]

thank you!!!

[xcstacy2]

I wanna give you a hug, THANK YOU!

[unisbushra]

can you help me in physics?

[Almudenaalcantara]

@unisbushra

There might be like 50 videos on physic at Sal's website at khanacademy. You will surely find what you need there.

[nactan]

@unisbushra google "khan academy"

[unisbushra]

can you help me in physics?

[TrueGuy]

My brain died for like 5 seconds while trying to figure it out, it was so much, but good info.

[birdpoo01]

For the second example, can't you just divide the top number by the second number (5/2=2.5) instead of having to go through all the steps?

I graphed: sin[.000 000 000 000 000 5x]/[.000 000 000 000 000 2x], and I got 2.5.

I also graphed: sin[9.87654321x]/[4.938271605x­], and I got 2. Hence, [9.87654321]/[4.938271605]=2. So why can't I just divide the top number by the bottom number? It's a lot easier.

[polyopulis]

@birdpoo01 because the 5 is inside of the sine function, it is basically sin(5x)/2x. You can't just divide out the 5. It happens to work in this example but it won't work in others.

[1073601]

that second example confused me

[urumqilik]

i am getting it.... lol plz show me some luv and dun delete my comments :-)

[MonaRocks09]

at 3:09, why is it -1? why didn't he plug in the zero?

[MyOverflow]

@MonaRocks09 He did plug in 0. 0 goes into the x terms, but since there was no x term, the 0 didn't have any affect.

It's like evaluating f(x) = 5, the value of x has no bearing on the answer.

f(2) = 5, f(32.762) = 5, etc.

[BannedLol4l]

I used values near 0 like 0.0000001 to try this.

[BannedLol4l]

I don't quite get why lim(x-->0) sin(x)/x = 1. I saw his proof and I understand it, but it only works in radians, because the pi's cancel out. But in the case of lim(x-->0) sin(5x)/2x if you use x in degrees the limit is not 5/2 but something like 0.043... I tried this with my calculator, and in radians, it gives 5/2, but in degrees, it gives something else. And yet, 0 degrees should equal 0 radians.

So where's the problem?

[akondude]

@BannedLol4l confused here as well

[krellor]

@BannedLol4l

When you go through the process of deriving (sinx/x)=1 you are specifying the exclusive use of radians. The inequality that is derived from the trigonometric structures is based on the use of radians on the unit circle, hence why x is in radians. While 0 degrees equals 0 radians, one radian does not equal 1 degree. You cannot assume that just because the two systems intersect at zero, that they are directly interchangeable in all situations.

[geneerinen]

Yes, I found that 13 minutes useful. Thanks Sal!

[cm3rt]

The last problem is not clearly explained... As soon as 8:20 hits, it all goes down hill. Like you 2x is equivalent to a = 5? I am still lost.

[xSebas6089x]

i do not fully understand the last problem...i dont know where the a=5x come from , how can you just set this equality? where does it come from?

[xSebas6089x]

also , what is a , thank you

[jimlov04]

By substitution of variables. He substitutes 5x and calls this expression a in order to get the whole expression on the form sin x / x which is 1.

[glacialmind101]

Another way to do it is to remove 1/2 bc/ its a constant and then multiply by 5/5, then remove the 5 ontop bc/ its also a constant. this leaves you with 5/2 lim x-->0 (sin5x)/5x which is the same form as (sinx)/x. So again you wind up with 5/2x1=5/2.

I like Sal's way better though.

[MrFlamingoo1]

i love how america's next top model is bookmarked on your mozilla ;)

[pokaymahn]

this was confusing.. ughh my brain

[Janac]

@pokaymahn really!? even with the clear way that sal explains his videos?

[bradinator83]

i plug this into my graphing calculator and when i trace the curve of the function it says that it is undefined at 0, why doesnt it say 5/2?? i'm positive that the equation is correct when i put it in, like the parenthesis and brackets are fine, so if any one can tell me that'd be awesome..thnx

[philjc54]

Hello bradinator83. The limit is just a value that the function approaches as x gets smaller and smaller, but it might not actually be defined at zero, as in this case. Sometimes it is, but not always. In this case the function approaches 5/2, so for 0.0001, say, the function is very close to 5/2, but for x = 0, it is not defined, because this value gives us a zero in the denominator.

Anyway, see some of Sals earlier limit videos as he explains this point much better than me.

[captainplanet999]

you sure you didn't f up on your math here? im a huge fan of your lectures, and frankly ive learned more from an hour of your vids then from my whole calc class (im taking it for the second time =[) but around 4:51 doesnt a negative in the absolute value actually mean the positive, so the -2 and the abs(x) would be (-2)*(+x)? if u pump it out like that then u get -3, but if you do it your way then it becomes (-1)-2(-x)/(-x)=1 for x=-1. maybe im wrong but this confused me on the principles of abs

[jianzzz88]

i noticed it too.. shouldnt absolute value be positive x and x as -x?

in this case shouldnt it be (-x-2x)/x which is still -3 though

[justinhunt233]

when you have an absolute value it means it could be -x or x so you set up two different equations. one where x is positive. one where x is negative. then solve

[famousmanbearpig]

@captainplanet999 i thought the same thing too, at around 4:51 he got it wrong.

[illestdesimc]

im still confused

i need to noe the simplest definition of a limit

and how its used in math

plz help

[BigCrazyDude2343]

Watch all his videos about limits in order, and you will understand. But make sure that you understand algebra and trigonometry 100pct lol.....

[Cwhite400]

When finding the limit your basically predicting where the function would land if it continued on the same path. by looking at where it was before and after the given point, you should be able to figure out where it should of been.

Its used in order to find points on a line that would otherwise not exist because of things like dividing by zero. i'm sure this is probably confusing on its own, keep watching, it can be a rough concept but once you grasp it, its basically all about algebra

[cookieeatbird]

Is there any neccesity to convert the answer in terms of a back to x.

Another words plug 5/2 into a, and whatever x equals would be the final answer?

[alankarmisra]

No, because 5/2 is not the value of a, but the limit of a (there's a difference). And since the limit of a is also the limit of x, we have the answer we need.

[thelastwords]

for the second problem, couldn't we just take out the 5/2 right away without adding the a variable?

[Vendresse]

It magically works in this case because we're looking for the limit when x -> 0 and because the variable change is linear, but don't think of it as a rule because it's not. For example, sin(5x)/2x is not equal to (5/2)*[sin(x)/x] , and the limits when x->1 (or probably any number different from 0) of those 2 terms are not equal either

[yanemailg]

CTRL + Z doesn't work for cancellation ?

[cookieeatbird]

it's like MS paint. Only cancels like 4 tasks.

Come to think of it I sometimes suspect that's actually what Sal is using.

[highpriest49]

good work man. keep up the cal vids

[woodenjaw]

What if you just take the derivitive of the top and bottom then plug in zero at10:49

[aerosmith0816]

d/dx sinx = cosx

d/dx 2x = 2

lim cos(5*0)/2 = 1/2

x->0

you get a different answer

[Yellowflyte]

Thanks Sal.

[Winsunn307]

Thanks Sal, very helpful.

[adis89]

Thank you very much. These tutorials are very helpful. I am glad I stumbled upon this YouTube page.

[Manu9324]

His name is Salman Khan

[clerlic]

Hello, Sal.

Unless you're finished with this pre-calculus playlist, could you make a video on lim x->infinity sqrt(n^2+2n)-sqrt(n^2+3n) ?

Thank you!

[jokumusic]

Waranle: His name is Sal.

Hey Sal, I noticed that starting from the last video, your penmanship has improved. :P

[Waranle]

Thank you alooooooooot Sam. where can i get that graphing calculator you were using?

[VaKaBonSenTi]

Hey Waranle, here is the link of the calculator Sal in using

[jrendoso]

where ?

[MonaRocks09]

@Waranle lol his name is Sal