Mean Girls Math Solved – A Trick to Find Limits | Outlier.org

L'Hôpital's Rule is a theorem that allows us to find the limits of indeterminate forms – an expression for which the limits of individual functions don’t tell us the limit of the whole expression. It states that the limit of 1 function over another equals the limit of the derivative of that function over the derivative of the other. This lesson on L'Hôpital's Rule (and how it resulted in the iconic Mean Girls moment), shows how it can make limits much easier to solve.

Chapters:
0:00 The Mean Girls Example
2:31 L'Hôpital's Rule
3:30 Using L'Hôpital's Rule
5:47 Solving The Mean Girls Example

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#Calculus #HannahFry #LL'Hôpital'sRule #MeanGirls #Outlier

[gristly_knuckle]

Look, I’ve learned it, and I’ve forgotten it. I’ve learned it again. And I forgot it again. Plato said to Meno, “All learning is recollection.”

[barnster]

Didn’t understand a word. But you say it so beautifully I had to watch until the end.

[murbard]

The limit isn't infinity, that would have been the answer to the quiz and it would mean there is a limit, just not one in R. The limit doesn't exist in a much stronger sense than that, as the right limit isn't the same as the left limit.

[SurprisedDivingBoard-vurz]

Why do you need to find limits. If you want to have a stable platform for a sphere the circular ring underneath is more stable. L hospital is if you take two sphere you need two rings or a single ring with the other side facing each other. Which means parallel lines.

[noursine]

without forgetting the condition that f and g are derivable on a and that both f(a)=g(a)=0

[alphalunamare]

I like the way You hold Your Pen, So un-American :-) I was in gym class once and broke my ankle, I was messing about and couldn't tell. So I went through a whole school day limping. At one point I was shouted at and shed a tear to the laughter of all and I said sorry Sir. I stepped on some wood, it was a woodwork class. I was going down the drive 20 mins slower than the rest and our Gytm teacher came to me and asked why I was so tardy. Please Sir I hurt my leg being silly earlier. Wow! He took me to the hospital in his own car and I ended up at home with a plastered leg. We called it 'H' ospital. It was only later as a Maths geek, that I learnt it could be called 'Ospital, that's how I learned to kid folk that I knew French. You have a natural talent for explanation, you did a slick slight of hand with the ink and that was as neat as your blots were blots :-) ( ummm if that don't sound right .. it was meant to ..um sound right Imean).

[SuperDeadparrot]

As x gets smaller, ln( 1 - x ) approaches -x. As x gets smaller, sin( x ) approaches x. So the numerator is approaching -2x. The denominator is basically sin( x )^2 which approaches x^2 as x gets smaller. So we get -2x / x^2 as x gets smaller. Getting smaller from the positive real side we get -2 / x, approaching -inf. Getting smaller from the negative real side we get 2 / abs( x ), approaching +inf. So limit does not exist.

[achristianson]

Terrence Howard the unqualified mathematician would poke holes in this

[andreisebastianmoldovan]

Seems that when x-->0, x>0, the limit is -infinity and when x<0, the limit is +infinity

[cmbryant]

lim x->0 = minus infinity. The first of the 3 final limits lim x -> 0 (x cosx - cosx -1) / 2 = (0 - 1 - 1)/2 = -1

[walkerrowe]

What a pleasant person. You make a good TV math person, if there is such a thing. One question: do you real do math using a pen and not a pencil?

[michaelandersen]

3:30 You can't use L'Hopital's Rule on the limit as x goes to zero of sin(x)/x because that limit is the definition of the derivative of sin(x) at x=0.

It is circular reasoning to use L'Hopital's rule for that limit because you are using the derivative to compute the limit, but since that limit is the derivative, so you have to first compute that exact limit to get the derivative in the first place.

[vijayraghavan]

We don't need LHospitals rule
We can use Taylor series expansion for ln(1-x) in t 1:46 he numerator and the whole expression would reduce to -2/x

[robertarvanitis]

L'Hôpital says "both go to zero? No problem! Which goes FASTER?!"

[michaelgonzalez]

See thenegative line on the feeding of a rular

[jmf]

Isnt it minus infinity??? This can be seen quickly if you remember that 1- cosx2 = sinx2, you can see then that the second part of the equation goes to minus infinity.

[sloughpacman]

By induction, the rule can be used again so taking the second derivative of the numerator and denominator gives a limit of 0.5! 😀

[antheroni]

You can't use L'Hopital's Rule to determine the limit of sin(x)/x as x goes to zero because that limit is used to prove that the derivative of sin(x) is cos(x). This woman is using circular reasoning.

[lwzfog]

Nazarin was right & you were horribly, horribly, wrong.