i was about to send valdug but. but i know all the answers. we all know all the answers. it's like asking which 2016 presidential candidate's PR team sleeps the least. im still asking for valdug.
IM LAUGHING, i’ll try to make these funny at least, to make it worth it
who’s the cuddler: “my hugs are only for special occasions,” skulduggery says. “WAIT NO NO THAT DOESN’T MEAN DON’T HUG ME,” skulduggery also says. i think valkyrie tends to initiate the cuddles but a lot of the reason is bc she knows (on a unconscious level, at first) that he needs it more than she does. ESPECIALLY post tdotl. i mean, on her end, she gets a cold and bony tooth brush that’s all angles and gentle mockery. on his, he gets valkyrie right where he needs her: safe. not bleeding, not crying, not hurting. warm against his cool check, soft curves against his sharp angles, her heartbeat steadily reassuring.
who makes the bed: there is one answer to this question and valkyrie scoffs, SCOFFS at the fact he wastes his time, literally every single day, making a bed that’s going to be messed up again. like, even in the series context im sure he gets annoyed when there’s not enough time to make the bed in her guest room before they leave for the sanctuary.
who wakes up first: skulduggery technically does not need to sleep, so he times his meditation periods so that he “falls asleep” around when val does and then wakes up hours before so he can spend at least, like, a good hour staring at her. he’s so gross. GROSS.
who has the weird taste in music: they think it’s the other, because skulduggery has a collection of really really obscure records he’s hoarded for decades and valkyrie listens to people with names he doesn’t understand. “why are they ‘21 pilots’ if there’s two of them, valkyrie?”
who is more protective: well, one did frequently threaten to murder people on her behalf on a bookly basis. i do think/hope val’s own protective urges kick in at some point and she starts her own ‘i will kill you if you even think about hurting him’ things, because that’s true bliss
who sings in the shower: val and she sounds like a dying, drowning cat. skulduggery is endeared. he hates himself for it, but he is so endeared.
who cries during movies: skulduggery literally can’t, so: val. but she hates anyone seeing her cry over movies so she’ll just like. glare at the wall with tears in her eyes.
who spends the most while out shopping: look valkyrie has both a giant fucking fortune and her bone husband’s back account to take from so i feel like she just buys EVERYTHING and it’s bad. it’s really lucky that they collectively have like, 8 houses.
who kisses more roughly: skulduggery is all, slow, gentle kisses with cupped faces and murmured sweet nothings which is very sweet and very nice but sometimes a girl just wants her neck bit, OKAY, OK?? she probably gets bruised by the amount of times they accidentally headbutt/smack teeth/etc while kissing. it’s good they’re anti pda bc no one wants to fucking see that disaster
who is more dominate: skeleton crew would all probably unanimously say val here, and im gonna deviate from that slightly and say both? girl aint interested in someone who is completely submissive to her. she SAYS she is, and that she wants some nice little puppet who never talks, but she wants an equal on every platform. skulduggery probably knows this. skulduggery probably thinks, on occasion, that no one is actually going to fit that exact level of equality that valkyrie wants. he thinks that his best friend never going to be satisfied, and an awful part of him is relieved she’s never going to find a Perfect partner because it means he can’t be replaced.
meanwhile he’s got valkyrie on her back during training and she, bright red (with exertion. clearly) flips him onto HIS back and considers grabbing him by his shoulders and smacking his skull against the floor until he gets it.
my rating of the ship from 1-10: (cady heron voice) THE LIMIT DOES NOT EXIST
I have a question about the limit in the movie mean girls. I know the limit doesn't exist and you use L'Hopital's rule, but could you provide more steps? Also I watched the directors cut and the answer that Caroline Craft got is supposed to be a reasonable answer if she misread the question. She didnt do the math wrong but she read the question wrong and she has glasses so it's supposed to be accurate. Would that make sense mathematically?
I cannot believe I spent an hour doing this at 4am, but here we go:
The limit Cady and Caroline had to solve was the following:
If you plug in 0 you’re left with an indeterminate form, so you can use L’Hopital’s rule to evaluate the limit, i.e. take the derivatives of the numerator and the denominator (separately, NOT using the quotient rule) and evaluate your result to find the limit. Doing that gives you the following (I crossed out a complicated expression bc I realized I could rewrite it using trig identities much more easily. Also, note that 1-cos^2(x) is equivalent to sin^2(x)):
Basically you’re left with a numerator of -2, a finite number, and a denominator that gets arbitrarily smaller as x approaches 0, so the limit does not exist.
So, Cady Herron was right. I guess your question is whether Caroline could have made a relatively simple mistake and wound up with -1 as the answer? Or like she could have misinterpreted the question?
I can’t see a mathematical mistake that would give her the answer -1, and if she accidentally read the minus sign in the numerator as a plus sign she still wouldn’t get -1. HOWEVER - if she read the minus sign as a dot (sometimes used as a multiplication sign) or totally missed the sign and assumed the terms were being multiplied, then she WOULD get -1. So if she interpreted the limit as:
Then her answer of -1 is indeed correct, thought it takes implementing L’hopital’s rule more than once to figure it out:
In summary, I suppose it’s plausible that (fictional character) Caroline did misread the question and do all the math correctly. She does wear glasses. I guess there’s no way to know since she’s fake and all, but I think the main point is Cady Herron found herself in this moment and realized being plastic was a vapid and hollow way to live life and this dramatic showdown helped her realize that. So for that, we should be thankful that Caroline Craft misread the question and the limit indeed did not exist.
Friends, I am pissed off. I am pissed off and it is 1:45 am. I am pissed off because of math and because of Mean Girls.
I am pissed off because of what an uninformed travesty this is.
You know what I’m talking about. Everyone on this site knows what scene I’m talking about. And I’m here to tell you that this scene got just about everything wrong except the answer.
The following is a rant of utmost nerd rage. It is a rant of someone who was happily submerged in the storyline until this absolute nightmare hit. You do not need to know calculus to read this rant. I will explain everything necessary, and will not explain anything that needs more than two sentences.
I am captain of my school’s math league, and I am pissed.
For starters, here is the problem
Simply put, a “limit” is the value the graph equals almost at the given point (0). It must equal this value from either side of 0. It doesn’t have to equal that number AT 0, but it must “converge” there from both sides of 0. Sometimes the limit will be an actual number. Sometimes it’s positive or negative infinity. Sometimes the two sides of the graph disagree, and the answer will be “does not exist”
I want to start by saying there’s a JOKE in calculus classrooms that the safest answer is “does not exist” A LOT of limit questions have the answer “does not exist” since A LOT of limit questions target a vertical asymptote. (I’m not gonna explain this any more than by saying the limit at a vertical asymptote is very frequently “does not exist”)
———————ACTUAL REAL WAY TO SOLVE PROBLEM BELOW. YOU CAN SKIP OR SKIM IT IF IT GIVES YOU A HEADACHE———————-
1) So what’s the start to attacking a limit question? PLUG IN ZERO. PLUG IN THE THING IT’S APPROACHING Because if it equals a REAL NUMBER (and doesn’t drop out of the domain on either side) THEN THAT NUMBER IS YOUR ANSWER. (btw, if the domain issue happens. Then the answer is DNE no sweat)
Here’s how. Look at the top. Mental math. ln(1) is whatever number “e” (2.71ish) has to be raised to in order to equal one. Luckily ANY NUMBER raised to “0” equals 1, so that first part is 0. The next part, the sine part, is also 0. Any self respecting mathlete knows this.
So the top is 0-0. Or just 0.
The bottom is an identity that equals sin^2(0). Sine of 0 is 0. 0 squared is 0. So the bottom is ZERO.
So you’ve got 0/0! You know what that tells you?
You can’t divide by zero, so there’s no answer for f(0), but that tells you nothing about the LIMIT ON EITHER SIDE. So you gotta do something called “L’Hopital” which is a technique that involves taking the derivative of the top and bottom separately and hoping that clears up the divide by 0 issue. (This would take too long to explain. Just trust me on the derivative part).
So now you gotta keep the x in place. The derivative of ln(1-x) is -1/(1-x). This was a combination of a derivative identity and chain rule. takes a bit of mental math. The derivative of sin(x) is cos(x).
The top has become -1/(1-x) - cos(x).
The BOTTOM (which we’ve already converted to sin^2(x)) becomes 2sin(x)cos(x) as per chain rule and derivative identities.
So you know what we’re looking at? (-1/(1-x) - cos(x))/(2sin(x)cos(x))
But the bottom is a recognizable identity. 2sin(x)cos(x) converts to sin(2x). So now it’s (-1/(1-x) - cos(x))/(sin(2x))
Now you plug in ALL OVER AGAIN.
(-1/(1-0) - cos(0))/(sin(2(0))) = (-1 - 1)/0
Horseshit. now it’s-2/0…not a number.
But now you have three options! Infinity, negative infinity, and DNE (does not exist). Because anything over (almost) 0 will shoot to an infinity. If the sides don’t agree on WHICH infinity, it’s DNE.
So now you take that denominator (sin(2x)) and plug in a number JUST BARELY ABOVE 0, AND ONE JUST BARELY BELOW 0.
The important thing is that the sign changes. It’s positive if you plug in 0.0000001 and negative if you plug in -0.0000001
So on the left, it’s a negative over a “negative 0”, which shoots to positive infinity. on the right it’s a negative over a “positive 0”, which goes to negative infinity. They don’t agree, so it’s DNE.
YOU GUYS SEE HOW MUCH WENT INTO THAT? IT’S A LOT TO DO MENTALLY. I WAS DOING IT MENTALLY AND HAD TO TALK IT OUT WITH MYSELF FOR LIKE 5 MINUTES. WHICH IS ABOUT A BAJILLION TIMES LONGER THAN EITHER GIRL.
IT’S RAGING TIME.
This girl has my UTMOST HATRED. BECAUSE HER ANSWER MADE THE LEAST SENSE IMAGINABLE.
NEGATIVE 1 SHE SAYS. -1! WOW. HOW?! WHY?!
BECAUSE EITHER—SHE PLUGGED IN 0 AND FORGET HOW SIMPLE TRIGONOMETRY WORKS TO SUCH AN EXTENT THAT SHE GOT BOTH THE NUMERATOR AND THE DENOMINATOR WRONG IN SUCH A MANNER THAT SHE THOUGHT IT SIMPLY EQUALED -1. (HOW??)
OR SHE L’HOPITALED IT AND…???? ?!?!?!?! I CANNOT THINK OF A SINGLE REASONABLE MISTAKE THAT WOULD LEAD YOU TO BLURT OUT NEGATIVE 1. SHE’S AN EMBARRASSMENT. I’M REVOKING HER MATH CARD.
But CADY. Cady is so much worse because her MENTAL MONOLOGUE MADE NO FRIGGING SENSE.
1) She says “How come I can’t remember anything about limits?”
HOLD THE FUCK UP CADY. That’s like getting into the pilot seat of a plane and saying “Why can’t I remember anything about how to push buttons?”
If you don’t know limits, you don’t know calculus. Go home. This is unforgivable.
2) She says “That was the week Aaron got his hair cut.” (my own emphasis)
No. No no. You do not spend “a week” on limits. You may as well spend “a week” on math. No. You spend months. And even then you HAVE TO REMEMBER WHAT THE FUCK A LIMIT IS TO DO CALCULUS.
IMAGINE TAKING ADVANCED CHEMISTRY AND NOT KNOWING WHAT AN ELEMENT IS.
“Okay what’s the molecular geometry of phosphoric acid? How many p orbitals and s orbitals in the bonds? Is it polar or non polar? What’s its conjugate base when dissolved in water?”
Cady, “Wow…why can’t I remember what phosphorous is?”
3) THE DIAGRAM ON THE BOARD IN HER MIND.
The board says “infinite limits”, and Ms. Norbury has drawn a diagram of a DNE. THAT IS NOT AN INFINITE LIMIT. THE TWO SIDES OUGHT TO BE CONVERGING TO THE SAME INFINITY. GOD.
4) Then this…CRINGE-WORTHY line:
“If the limit does not approach anything…then the limit does not exist!”
What. calc. class. did. you. take?
“does not approach anything” PAH. MATH TEACHERS ARE ROLLING IN THEIR GRAVES.
THAT’S NOT AN EXPLANATION YOU UNCULTURED SWINE.
She could have said “if the two sides approach different infinities” then maybe I could let her horseshit slide. but no. “The limit does not approach anything”
There is no limit. SO HOW IS IT DOING ANYTHING TO START?
THE RIGHT HAND LIMIT APPROACHES SOMETHING. THE LEFT HAND DOES AS WELL. GOD. THEY JUST DO NOT AGREE.
And she says it like it’s a frigging EPIPHANY.
HOW THIS SCENE SHOULD HAVE GONE:
“Wow. I really was not paying attention in class. I don’t understand the first thing about calculus. I certainly haven’t tried plugging 0 in. I don’t know how to do L’Hopital. I do not understand derivatives. I know nothing about trig identities. I literally do not have the facilities to even approach this problem. But I remember some random answer my teacher said is sometimes right. I’m gonna grit my teeth and make a blind guess and hope I’m right.”
Look, I know it’s a MOVIE. I know they’re not looking to bore their audience with ACTUAL MATH. But this is just SLOPPY. LAZY. INSULTING.
“I’m actually really good at math!” —Cady Heron, a huge freaking liar.