2) 2:58 SOMETIMES the product of two negative INTEGERS is a positive? You mean always and any two terms, asshole.
3) 3:38 almost all the marks on a test is given for working. In fact, the Jun 2010 exam only offered 10% for correct answers in my exam board (UK, but still.)
4) 6:19 this isn't really the hardest algebra I've ever seen. I have no complaints here.
@KoushOWNs lol its so easy, and she's probably wrong. If you were to use l'hoptals rule you could likely find the limit instead of saying its undefined.
all you need to look at is the bottom. If the bottom is zero, you know you can't divide by zero. (x is approaching zero so replace all the "x"'s with 0 on the denominator)
@KoushOWNs oh ya btw, just did L'hopitals rule and it doesn't work because by the time I reached the second derivative, I couldn't use it because L'hopitals only works under the condition of 0/0 or infinity / infinity
This movie is supposed to be about calc, but they dont talk about derivatives, the most basic part of calc, or integrals. The farthest they got was limits, and they were cake...
I can't believe a human can do that in their head! Were doing limits now and I can't imagine solving limits in my head while imagining women! Gah! Movies!
hahah I like how she solved it. The great realisation was that it doesnt approach anything. How d she get that did she plot the function in her fuckin mind??
anyway L'Hospital JUST ONCE and you get zero denom and finite numerator. end of story
I get 1/2 as the limit. First, the denominator is just sin^2. As the limit is of form 0/0, use L'Hospital's rule. The numerator becomes 1/(x - 1) - cosx. The denominator will become 2(sinx)(cosx) which equals sin(2x). Again the limit is of form 0/0 so use L'Hospital's rule again.
The numerator is now (x - 1)^(-2) + sinx. The denominator becomes 2cosx.
plug zero into the equation. numerator = (0 - 1)^(-2) +sin(0) = 1 + 0 = 1
I am. I originally put together these clips for a class of mine, a math appreciation type class, as a sort of introduction, to start the semester thinking a little more broadly and realistically about how math fits into our lives than is typical. Also as a little bit of an antidote to the usual pop math fare.
If so, wow. lol. I think it would be pretty cool to have a teacher to get us to watch Mean Girls and then discuss or talk about it, not that math wasn't already cool in high school.
@LilMarkymark L'Hopital's rule is only applicable when the limit of the derivatives exists at that point. That the limit you get when doing L'Hopital's doesn't exist does not mean that the original limit does not exist. It only implies that you can't use L'Hopital's rule to try to find the limit. See Wikipedia's entry on the rule, where they use the example f(x) = x + sin(x) and consider when x -> infinity. The limit of f(x) exists, but if you use L'Hopital, you get a non-existent limit.
@maximalideal Not quite right. If the limit via l'hopitals exists OR the limit by l'hopitals approaches infinity then you can use it. If the limit does not exist for any other reason when you have used l'hopitals then l'hopitals is an invalid method. Also, to confuse you further look at this example: lim x to infinity of f/g where f(x) = e^-2x(cosx + 2sinx) and g(x) = e^-x(cosx + sinx) . f'/g' has limit 0 but this limit actually does not exist! I avoid l'hopitals where i can .... it is risky!
@maximalideal This problem is quite easy WITHOUT l'hopitals ... it is ~ [landaus symbol] to -1 / [2sin(x)] as x-->0 and this limit clearly doesn't exist.
Holy crap! When Kady is walking into spring fling and you see the shot from the from her arm arent in her jacket but when they show her from the back she is!
HAHAHA OMG! I know the place where they shot the mathlete competition scene! It's Con Hall!! :O lol I actually have lectures in there! So, I've sat in that place before.. feels weird to see it in a movie actually
If you evaluate this it is indeterminate, at 0/0. However, if you use L'Hospital's Rule, it simplifies to the form of -2/0, or negative infiniti. From the derivative it tells us that the value of the numerator infinitely approaches 2, while the denominator approaches 0.
lol it isn't that it approaches nothing, it's that it appraoches different things from both sides. someone who wasn't even paying attention to limits in class wolud never be able to solve that
wow, they must have gone a long way to get to that mathletes competition because that building is convocation hall found on the University of Toronto campus in Toronto, Canada. I was just there for my bio class this morning lol.
so uh the answer in infinite from one side and negative infinite from the other side after a Lhopitals rule and you get limit does not exist. dang she did it quick though for someone who didnt know what she was doing
@maximalideal actually you don't even have to worry about taking the limit from both sides. Use L'Hospital's rule, multiply the top and bottom of the resulting limit by (x-1), you have 1-sin x on the top, which equals 1, and the bottom equals 0, which does not exist therefore the limit does not exist.
@LilMarkymark17 L'Hopital's rule is only applicable when the limit of the derivatives exists at that point. That the limit you get when doing L'Hopital's doesn't exist does not mean that the original limit does not exist. It only implies that you can't use L'Hopital's rule to try to find the limit. See Wikipedia's entry on the rule, where they use the example f(x) = x + sin(x) and consider when x -> infinity. The limit of f(x) exists, but if you use L'Hopital, you get a non-existent limit.
sub in x=0 to find your limit. ends up being (loge(1)-sin0)/(1-1^2), which ends up being (0-0)/0, and as you're dividing by zero the limit does not exist!
@lookche You can't say the limit doesn't exist just because (0-0)/0 is undefined. 0/0 is an indeterminate form and you need to use L'Hospital's rule to determine whether the numerator or denominator reaches 0 first, or neither. For example, (e^x-1-x)/x^2 is also 0/0 as x->0, but the limit is actually 1/2.
@scholzie well as x->0 from small, negative values of x, x approaches infinity. and as x->0 from small, positive values of x, x approaches negative infinity. there is clear asymptotic behavior at x = 0. it's easy to ascertain that there is no limit in this equation due to its normal behavior.
@SubImpactt The limit of that equation as it approaches x from the left is -1. However, the limit does not exist as x approaches 0 from the right. For the limit to exist, the side limits must be equal. They are not so therefore the limit does not exist for function f as x approaches 0
sin(x) behaves like "x" (linear function) around the 0, which means that for a very small x it's either a very small positive number or a very small negative number. however what that means is that the inverse of that function (=1/x) is either positive infinity or negative infinity.
sin(x) behaves like "x" (linear function) around the 0, which means that for a very small x it's either a very small positive number or a very small negative number. but the inverse of that function (=1/x or in our case -1/sin x) is either positive infinity or negative infinity.
Don't let the haters stop u from doing your thang !! Lol
TrayDay101 1 day ago
1) Lindsay Lohan is so hot here.
2) 2:58 SOMETIMES the product of two negative INTEGERS is a positive? You mean always and any two terms, asshole.
3) 3:38 almost all the marks on a test is given for working. In fact, the Jun 2010 exam only offered 10% for correct answers in my exam board (UK, but still.)
4) 6:19 this isn't really the hardest algebra I've ever seen. I have no complaints here.
5) 6:47 147 is also correct.
6) If you know anything about limits, this requires no working out.
BleedingLlama 4 days ago
CON HALL.
storm610 4 days ago
if the limit did not exist in a math problem, my teacher would just say "the answer to number 5 is mean girls"
summerluverr 1 week ago 3
@summerluverr best comment ever!
eternalnight100 1 week ago
That wasn't exactly a hard question for a maths championship
Shazgi 2 weeks ago
OMFG She was so hot in this fucking movie.
gmlmangwar 4 weeks ago
GET SOME~~~~~~~~~
iluvthatmusic 4 weeks ago
WASSUP
wookieproductions 4 weeks ago
This might be the dumbest thing I've ever seen.
Everyone needs to go on Wolfram Alpha and plug this problem in and figure out that it actually is -1. Poorly made movie.
xS0L1DSH0Tx 1 month ago
how the hell did she get "the limit is negative one" ?
MrMbogza 1 month ago
Oh wow, I'm such a nerd, I actually knew what they were talking about....
TheNightsMoon 1 month ago
@TheNightsMoon Why is that makes you a nerd? It makes you matematicaly educated.
Mergahuszarok 1 month ago
@Mergahuszarok well fucking said
gigijbijbj 1 month ago
thang
rabbitcfh 2 months ago
LOL can't use L'hopital twice for this one just realized xD
su627 2 months ago
OMG thats my school!!! It's university of Toronto LOL xD and the limit is 1.....she had to use L'hopitals rule twice hehe
su627 2 months ago
@su627
Haha Con Hall!!!
chris110012 2 months ago
love this!
LeonLovesIt 2 months ago
at 7:14 you can totally see camera men XD
shelbsterrox 3 months ago
how the hell did she know that crazy ass limit doesnt approach 0?!
KoushOWNs 3 months ago
@KoushOWNs lol its so easy, and she's probably wrong. If you were to use l'hoptals rule you could likely find the limit instead of saying its undefined.
all you need to look at is the bottom. If the bottom is zero, you know you can't divide by zero. (x is approaching zero so replace all the "x"'s with 0 on the denominator)
andr00123 2 months ago
@KoushOWNs oh ya btw, just did L'hopitals rule and it doesn't work because by the time I reached the second derivative, I couldn't use it because L'hopitals only works under the condition of 0/0 or infinity / infinity
andr00123 2 months ago
I hate limits @@
mylinhle801 3 months ago
LOL I love how I never understood it until I took calculus last year and I'm like "I know what that means now!"
tiptopluongo 3 months ago
we'd like to get jackets.
Autonova 3 months ago
It's Con Hall!!!
holaperu1000 3 months ago
On Oct. 3 he asked me what day it was.
aevelynl95 3 months ago
im watching this on october 3rd :O
rowergirl2011 3 months ago
This movie is supposed to be about calc, but they dont talk about derivatives, the most basic part of calc, or integrals. The farthest they got was limits, and they were cake...
Scooperson6988 4 months ago
OMG That Con hall in the final math battle :D
layser49 4 months ago 2
Lmao at 8:38
Selenafreak67 4 months ago
girls are super mean all right. Lol, check out my vids !!!
OneDayHenry 4 months ago
I'm using this to review for AP Calc.
tehsummit 4 months ago
great turn out this year
JaceyNaii 4 months ago
i kid you not in my math class once my teacher mentioned limits and literally half the class went "the limit does not exist!"
cessnacitationx1 5 months ago 12
This has been flagged as spam show
The math competition was filmed at Con Hall. U of T represent!
chubbest28 5 months ago
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chubbest28 5 months ago
i came back to this problem since i learned calc and its actually really easy
whiteelf75 5 months ago 6
press 7:54 then 8:56 lol
ambyleeful 6 months ago
How are these people so smart?
puffballs839 6 months ago 2
Thumbs up if you're watching this in 2011 :D
YaraSoWhat 7 months ago 34
I LIES NO DO
RvStacks1 7 months ago
...we pick the girl too
ayatollahrocknrolla 7 months ago
damn africaa hahahaahah
Cosidelight 7 months ago 2
sucks
angeldeoro18 8 months ago
I almost can't handle how many people are saying Hospital instead of Hopital lol.
Flound3r 8 months ago
I can't believe a human can do that in their head! Were doing limits now and I can't imagine solving limits in my head while imagining women! Gah! Movies!
Nickuncle 8 months ago
lindsey lohan doing calculus hahaha
MaverickBearage 9 months ago 8
just noticed that tina fey is the teacher lol
purpleogtwi 9 months ago
hahah I like how she solved it. The great realisation was that it doesnt approach anything. How d she get that did she plot the function in her fuckin mind??
anyway L'Hospital JUST ONCE and you get zero denom and finite numerator. end of story
h0wud0in2 10 months ago
1) Double differentiate both numerator and denominator with respect to x (applying l'Hopital's rule
2) -1/2/2
3) ????
4) Profit
revilo314 10 months ago
GET SUUMMM, GET SUUUUUUUUMMMM!!!
Darko1393 10 months ago
I get 1/2 as the limit. First, the denominator is just sin^2. As the limit is of form 0/0, use L'Hospital's rule. The numerator becomes 1/(x - 1) - cosx. The denominator will become 2(sinx)(cosx) which equals sin(2x). Again the limit is of form 0/0 so use L'Hospital's rule again.
The numerator is now (x - 1)^(-2) + sinx. The denominator becomes 2cosx.
plug zero into the equation. numerator = (0 - 1)^(-2) +sin(0) = 1 + 0 = 1
denominator = 2cos(2*0) = 2 * 1 = 2
Therefore the limit is 1/2
urimv 10 months ago
@urimv
-1/2
you forgot to apply the chain rule to the first term. :p
revilo314 10 months ago
Ah yes highschool
GabiN64 10 months ago
ew math is gross. however i appreciate those who are good at it. rock on you guys who dont totally suck ass at math.
jamerikan5689 10 months ago
I am. I originally put together these clips for a class of mine, a math appreciation type class, as a sort of introduction, to start the semester thinking a little more broadly and realistically about how math fits into our lives than is typical. Also as a little bit of an antidote to the usual pop math fare.
maximalideal 10 months ago 7
If you don't mind me asking, are you a teacher?
If so, wow. lol. I think it would be pretty cool to have a teacher to get us to watch Mean Girls and then discuss or talk about it, not that math wasn't already cool in high school.
neogeo328 10 months ago
This has been flagged as spam show
Developing the functions in Taylor series gives:
ln(1-x) = -x+O(x²)
sin(x) = x+O(x³)
cos²(x) = 1-x²/2+O(x⁴)
f(x) = (ln(1-x)-sin(x)) / (1-cos²(x)) = (-2x+O(x²)) / (x²/2+O(x⁴)) = -(4+O(x)) / (x+O(x³))
The term of least degree weights heaviest close to zero so the limits equal:
lim (x->0⁺) f(x) = lim (x->0⁺) -4/x = -4/0⁺ = -∞
lim (x->0⁻) f(x) = lim (x->0⁻) -4/x = -4/0⁻ = +∞
Left and right limits are different so the limit does not exist. =)
HaraldNordgren 11 months ago
she's right. ln(x-1) moves the function so that x can not approach 0, therefore the limit does not exist at x approaches 0
watusernameshudiuse 11 months ago
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watusernameshudiuse 11 months ago
Comment removed
watusernameshudiuse 11 months ago
This has been flagged as spam show
Thumbs up if you were sent here by YOUR CALC TEACHER!
drfitzenstein 11 months ago
THEY WANT JACKETS
h0lyshitters 11 months ago
oh common!! how could anybody solve the first 2 problems in something like 5 seconds??
h0wud0in2 11 months ago
LOLLL
EvangelineBeatrice 11 months ago
That's a tall ass asian
jaytothelu 11 months ago
What's the name of the beat at 9:08 ? I've heard it in another movie.
SnookTX2010 11 months ago
That asian kid's name is so close to Tupac
theredheadchannel 1 year ago
7:57 That killed me!!! ' Oh crap i lost! "
gleekfuzz 1 year ago
@LilMarkymark L'Hopital's rule is only applicable when the limit of the derivatives exists at that point. That the limit you get when doing L'Hopital's doesn't exist does not mean that the original limit does not exist. It only implies that you can't use L'Hopital's rule to try to find the limit. See Wikipedia's entry on the rule, where they use the example f(x) = x + sin(x) and consider when x -> infinity. The limit of f(x) exists, but if you use L'Hopital, you get a non-existent limit.
maximalideal 1 year ago 15
@maximalideal Is it wrong that i think this comment is the only comment in all of Youtube that is relevant in ANY way?! :D
PortCactus 7 months ago
@maximalideal Not quite right. If the limit via l'hopitals exists OR the limit by l'hopitals approaches infinity then you can use it. If the limit does not exist for any other reason when you have used l'hopitals then l'hopitals is an invalid method. Also, to confuse you further look at this example: lim x to infinity of f/g where f(x) = e^-2x(cosx + 2sinx) and g(x) = e^-x(cosx + sinx) . f'/g' has limit 0 but this limit actually does not exist! I avoid l'hopitals where i can .... it is risky!
sam5248 7 months ago
@maximalideal This problem is quite easy WITHOUT l'hopitals ... it is ~ [landaus symbol] to -1 / [2sin(x)] as x-->0 and this limit clearly doesn't exist.
sam5248 7 months ago
My correction it is ~ -2/sinx as x-->0
sam5248 7 months ago
lmao at Kevin G at 8:38
pigglywink 1 year ago
fuck every girls lives, the guy who plays aaron is gay.
happyhappydancer12 1 year ago
P!nk song!! lol
RebaWillGraceFan 1 year ago
I just realized that on the card Kevin Gnapoor gave to Cady, it says "Bad-Ass M.C." on the right xD
twilightgirl6271 1 year ago
heey October 3rd is MY birthday! lol :D
hotdarx 1 year ago
it's raining.......yeah
fianlfantasyx2lover 1 year ago
is there suppose to be camera men at 7:14???!!!!!!
CarlyxCrash 1 year ago
@CarlyxCrash those aren't cameras, those guys are carrying the podiums
pkap9041 1 year ago
HEY 5:33 is filmed at my school ! University of Toronto COOL!
haha i looove this movieee
xxVeronica92xx 1 year ago 3
@xxVeronica92xx
Did you know The Naked Mile was filmed at Con Hall?
And the army scene from The Incredible Hulk was at King's College Circle. =)
MissIyer 1 year ago
The music at 3:05 is in Willy Wonka and the Chocolate Factory...
rebskie1 1 year ago 2
"Grool!"
Nice catchphrase there!
DorvellTStewart 1 year ago
HAHAHAHA! indian boy is so funny!! lolzz! and the gurl wit deh uniform is so ugly!! YUCK! make over
livi1226 1 year ago
haha check out kevin's card. math enthusiast and badass mc!
Deeperella 1 year ago
Holy crap! When Kady is walking into spring fling and you see the shot from the from her arm arent in her jacket but when they show her from the back she is!
Uhthenuh 1 year ago
The limit is "negative infiniti"... Use Taylor series !
Mithrawnuruodo 1 year ago
@ comments below: thank you for turning this clip into a math lesson!
DevilDude16 1 year ago
Lindsay used to be so beautiful. Now she looks haggard. Let this be an example of what drugs and alcohol will do to you.
SimplyRisque 1 year ago 3
@SimplyRisque
A bit ironic how her limits didn't exist.
Michael326 1 year ago
We were learning limits today, and all I could think about was this movie LOL
ronniemonnie 1 year ago 39
@ronniemonnie Same!
tehsummit 4 months ago
HAHAHA OMG! I know the place where they shot the mathlete competition scene! It's Con Hall!! :O lol I actually have lectures in there! So, I've sat in that place before.. feels weird to see it in a movie actually
915jefflee 1 year ago 6
@915jefflee yeah that's con hall right by sf,
<3 uoft
TheDreamer201 1 year ago
is this for some school project lol? yeah we always quote the limit does not exist in math class.
atims05 1 year ago
the limit doesnt exist.. cause they will never be equal to each other... i love calculus AP
123abigal 1 year ago
I fucking hate math.. I could barely pass PRE ALGEBRA.
ifuseekamy 1 year ago 4
@ifuseekamy thank you!one person who doesnt say its easy!
MishMishgangsta 1 year ago
im sorry but when kevin talks ´cool´ its like akward ya no i have no affense to the kids he rocks but like its kinda akward
SweetStuffDiamond 1 year ago
I hate calculus.
KathRou27 1 year ago
Hahaha.
She wiped her hand on her trousers @ 8:36
Guard0985 1 year ago
@Guard0985 ahaha, out of all the times i've watched this movie, i never noticed that she wiped her hands after shaking hands with the other girl.
that was pretty funny, haha.
sweetluv322 1 year ago
it's raining...yep
TheAwesomenated 1 year ago
lol this is my favorite movie XD! its raining.. yeah..
ClythiaMystica 1 year ago
This is how to solve the limit:
If you evaluate this it is indeterminate, at 0/0. However, if you use L'Hospital's Rule, it simplifies to the form of -2/0, or negative infiniti. From the derivative it tells us that the value of the numerator infinitely approaches 2, while the denominator approaches 0.
-1.9999999999/ .00000000001 = f(x) > - 1,000,000 < f(a)
The simplified form is -1-cosx/x2cosxsinx which does not exist as it approaches negative infiniti
Tim92G 1 year ago
Comment removed
Tim92G 1 year ago
4:22 Wicked quote! Probably just coincidence, but I was pleased.
Sungoddess18 1 year ago
if i ever win a math competition...i gonna rip my shirt
barkleysound 1 year ago
LOL! HOW YOU LIKE ME NOW!? *RIPS SHIRT* YOU LIKE THAT?! YEAH GET SOME! GET SOME! XD
Joschmo939 1 year ago
I love how every comment is about the math contest and the part where Lohan says that the limit does not exist.
ianonavy17 1 year ago
The limit does not exist!
MegaShiny 1 year ago
Mean Girls inspired me to take AP Calculus in 11th grade.
Best decision ever. :D
d0msp3ll 1 year ago
"How you like me now uh ,you liek that get some ,get some" lolsx!
Girlyy011 1 year ago 3
hmm apparently a 58% is a D??
subway987 1 year ago
I remember when I first learned limits, I thought of this movie
yankees032778 1 year ago 2
@yankees032778 me too! haha
frapevip 1 year ago
THE LIMIT DOES NOT EXIST.
kimberleexx3 1 year ago
8:56 asian guy gets his screen time LOL!
"what?" hahahaah
MGameSwim 1 year ago 72
@MGameSwim i actually thought this when i first seen this film :')
sophieSPAZZTARD 1 year ago
@MGameSwim lol. But at the start, he also says.."I hear her hair is insured for ten thousand dollars".
RorySeizeTheDay 1 year ago
@MGameSwim but theres also the bit when he says that regina's hair is insured for $10,000
jackchrisevans 1 year ago
I used to think it was some crazy hard shit when i first saw this movie. Then i took Calc and it was so simple.
On a sidenote, look at how much of a suckulent red head linsday lohan is in this movie. Now she's pretty fucked up.
my89tube 1 year ago 2
its undefined, right?
Krinks86 1 year ago
THE LIMIT DOES NOT EXIST!!!
kingsterbomb 1 year ago
"if the limit doesn't approach anything"
lol it isn't that it approaches nothing, it's that it appraoches different things from both sides. someone who wasn't even paying attention to limits in class wolud never be able to solve that
lynxiness 2 years ago 47
8:40 best bit of the film
JaceyNaii 2 years ago
wow, they must have gone a long way to get to that mathletes competition because that building is convocation hall found on the University of Toronto campus in Toronto, Canada. I was just there for my bio class this morning lol.
redbathtubs 2 years ago
HAHA lindsay lohan and smart in the same movie.wow
RiseToNothing 2 years ago
so uh the answer in infinite from one side and negative infinite from the other side after a Lhopitals rule and you get limit does not exist. dang she did it quick though for someone who didnt know what she was doing
SparkyFlary 2 years ago
6:04 STILL MAKING ME LAUGH LIKE CRAZY
coolboyaznkid 2 years ago
Soo you got pretty involved with the meaning of a PG13 chick flick...good video though
emmmmih 2 years ago
5:38 LOL
HK6 2 years ago
she was soo lucky with that math problm,, the explanation she thinks of is NOT how you solve limis,, hehe
luvvv the movie though
amparobarrio 2 years ago
lol the limit of that equation is negative one
SubImpactt 2 years ago
you have to take the limit from both sides.
maximalideal 2 years ago 30
@maximalideal it's still -1
mariuschhh 1 year ago
@maximalideal actually you don't even have to worry about taking the limit from both sides. Use L'Hospital's rule, multiply the top and bottom of the resulting limit by (x-1), you have 1-sin x on the top, which equals 1, and the bottom equals 0, which does not exist therefore the limit does not exist.
LilMarkymark17 1 year ago
@LilMarkymark17 L'Hopital's rule is only applicable when the limit of the derivatives exists at that point. That the limit you get when doing L'Hopital's doesn't exist does not mean that the original limit does not exist. It only implies that you can't use L'Hopital's rule to try to find the limit. See Wikipedia's entry on the rule, where they use the example f(x) = x + sin(x) and consider when x -> infinity. The limit of f(x) exists, but if you use L'Hopital, you get a non-existent limit.
maximalideal 1 year ago
sub in x=0 to find your limit. ends up being (loge(1)-sin0)/(1-1^2), which ends up being (0-0)/0, and as you're dividing by zero the limit does not exist!
lookche 1 year ago
@lookche You can't say the limit doesn't exist just because (0-0)/0 is undefined. 0/0 is an indeterminate form and you need to use L'Hospital's rule to determine whether the numerator or denominator reaches 0 first, or neither. For example, (e^x-1-x)/x^2 is also 0/0 as x->0, but the limit is actually 1/2.
scholzie 1 year ago
@scholzie well as x->0 from small, negative values of x, x approaches infinity. and as x->0 from small, positive values of x, x approaches negative infinity. there is clear asymptotic behavior at x = 0. it's easy to ascertain that there is no limit in this equation due to its normal behavior.
lookche 1 year ago
@scholzie @scholzie graphing the equation also gives the answer.
lookche 1 year ago
@SubImpactt The limit of that equation as it approaches x from the left is -1. However, the limit does not exist as x approaches 0 from the right. For the limit to exist, the side limits must be equal. They are not so therefore the limit does not exist for function f as x approaches 0
tong135799 1 year ago
@SubImpactt no itso not.. L Hospital and you get (-1/x -cosx) / (1+2cosx sinx) and x->0 so denominator one numerator goes to infinity
h0wud0in2 11 months ago
@SubImpactt So lindsey is correct, here's why
start with the easy part:
ln(1-0) = ln(1) = 0
now the denominator:
1-cos^2 x = sin^2 x
so that leaves us with:
lim x->0 (-sin x) / (sin^2 x) =
lim x->0 (-1) / sin x
sin(x) behaves like "x" (linear function) around the 0, which means that for a very small x it's either a very small positive number or a very small negative number. however what that means is that the inverse of that function (=1/x) is either positive infinity or negative infinity.
rudekult 10 months ago
This has been flagged as spam show
@SubImpactt So lindsey is correct, here's why
start with the easy part:
ln(1-0) = ln(1) = 0
now the denominator:
1-cos^2 x = sin^2 x
so that leaves us with:
lim x->0 (-sin x) / (sin^2 x) =
lim x->0 (-1) / sin x
sin(x) behaves like "x" (linear function) around the 0, which means that for a very small x it's either a very small positive number or a very small negative number. but the inverse of that function (=1/x or in our case -1/sin x) is either positive infinity or negative infinity.
rudekult 10 months ago
Kevin is a badass
MonkeyOctober 2 years ago
8:38 best scene ever
Mooktopia 2 years ago
I love that mathlete Kevin.
He's actually really cute.
XD
Beatmyguest001 2 years ago
thanks! i was actually looking for most of these scenes! LOL!
tarynlau 2 years ago
Nice xD
What's the name of the Soundtrack at 9:05?
inkassso 1 year ago