anonymous asked:

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.

Originally posted by imaginerandomocity


hey all! to cut a long story short, my mother kicked me out and im in need of money for living costs+paying board to my partner and his father for letting me stay with them. this is the only way i can earn money right now!

to compliment the recent release of pokemon sun and moon im opening up some personalised pokemon trainer commissions! basically a pre-established character OR your own trainer design OR an original character of your choice + their favoured partner pokemon together looking cool n stuff!!

full body clean sketch + no colour = 10$ AUD

full body clean sketch + colour and any other effects (fire, water etc.) = 25$ AUD

full body clean sketch + FULL TEAM OF POKEMON + colour and any other effects = 35~40$ AUD (depending on complexity of pokemon!) keep in mind this option may take a while to complete as well! (1-3 days approx)

hmu with an email at forartblog@hotmail.com or send me an ask/IM here on tumblr if youre interested (i suggest sending an email, the tumblr ask system is unreliable)! all prices in AUD (australian dollar) thru paypal only, payment received after rough sketch!

disclaimer/some things to note: my style is somewhat unpredictable/inconsistent in that i draw how i percieve a character/facial features, i operate on AWST (Australian Western Standard Time) and i reserve the right to refuse any commission.

the drawings seen above can be viewed in full here, here and here! my regular, non-pokemon themed commissions page can be viewed here!

thank you so much for your time!


I should make it an infamously known fact that I despise drawing stitches and that Japanese armour is my mortal enemy. Even with the duplicate button on hand it’s still TEDIOUS WORK.

care for some BG commentary?

reason #289 that this whole thing is fake: I had a bunch of dead shifts at work so I spent a godforsaken number of hours searching FB for pictures of “Freddie” outside of the Tammi/Briana/Ashley bubble. And I mean, I was piecing together their family tree going back 3 generations so I could find relatives far and wide on FB lol I didn’t post this on my own blog because we know this is fake already and people would probably give me shit for searching so hard but like, I was bored and I’m nosey af so whatever.

I was determined to find pics of Freddie that either made this whole thing look more legit like he’s a real family member, or a mistake-picture like if he is genuinely related to the Clark’s I’d find a picture on an obscure friend/relative’s account where he’s mislabeled with his real name or something. Anything at all that shows he’s part of that family, whether he’s really related to them or it’s just part of the act, you know?

And I found ONE. ONE SINGLE PICTURE! in all of their family and friend’s facebook accounts. I found one uncle with a pic of him holding “freddie” (I think it was Brett’s brother if I remember my search correctly). How unrealistic is that? A whole year of this baby being around and he doesn’t show up in the background of any family gathering pictures, he’s never mentioned by anyone, there isn’t a single mention of “the newest member of the family” or LITERALLY ANYTHING. The kid genuinely does not exist outside of Tammi/Briana/Ashley’s posts.

It’s just not how real life works! I know this has been screamed about before but it just is funny that they thought this out so poorly. If they wanted to make this idiot-proof Tammi and Brett should have become legal foster guardians of a newborn so the baby would really look like part of the family for a year or two and B would have real things to document at weird times of day & night like messy feedings and sickness and tantrums at 3 a.m. like you know, things normal parent’s have to deal with… but all we get from B is perfectly happy/staged pics and nothing in between that shows what life is really like with a newborn - but it all just goes to show they really didn’t think this would go on for so long. 

When we have babies they show up in our friend’s pictures because they’re excited to meet our kid, especially the first kid! Relatives, especially in the first few weeks, take so many pictures with the newborn, it’s always a time that’s well documented. But “Freddie” genuinely does not exist to anyone outside of those three women.

As an example of this, our newest family member just turned 1 and I went on my sister’s FB and looked through her friends list and it took a total of 15 minutes to find 6 other people that had a picture of her baby in one of their own albums. Because the baby is real and real interactions happen and nobody has a reason to be shady and act like the baby doesn’t exist. 

Damn, anon. I’ve nothing to add. Great points and great job. I’m just here like:

Originally posted by i-am-a-lucky-artefact

  • yikes

i was tagged by @foxyholidays (thanks bud) and i am sorry if anyone actually listens to this because i found out i sound like a twelve year old boy today

>Name and username
>Where are you from?
>Pronounce the following words: Exy, Palmetto State University, Minyard, Eden’s Twilight, Renee, Excites, Tetsuji Moriyama, Jean, Racquet, Rebound, Bodycheck, Match, Riko, Yakuza, Butcher, Stadium, Foxhole court, Sakavic, Easthaven, Nathaniel Wesninski, Andreil, Blood, Wymack, Cuts, Dashboard Lighter, Cracker Dust, Binghamton, Baltimore.  
>When did you read the series?
>How did you find out about it?
>Read a passage from the books
>Favourite quote
>Favourite scene
>Favourite character
>Name one headcanon you’re invested in
>Choose one AU
>The scene that destroyed you the most
>How fast did you guess the main ship of the story?
>Have you made friends in the fandom?
>End with the team you’d like to play for + position

i tag @jerememeknox @ohmoreau @yikesmoreau @isakbaby @rikomoriyamaofficial @androominyard @palmetostate


Colmar, France.

Because I’m the luckiest jerk in all the world, I set off to Switzerland for Thanksgiving break. And because I’m a lucky jerk who works the system sometimes, I extended my trip by a couple days and ended up spending the extra time in France (because oh man, Switzerland is expensive). We ended up in Colmar in the Alsace region of France. It’s 30 minutes from the German border and about an hour by train from Switzerland.

This town is straight out of Beauty & the Beast. We were singing a medley of songs the entire time we were here. It’s just so charming and beautiful and fairytale-like. 

This was one of the most low-key international trips I’ve ever been on. So, we spent the majority of our time just wandering the quaint streets, drinking coffee, and eating pastries. And I won’t lie, we did spend a fair bit of time in our cute little apartment. One day we did take the bus 40 minutes to Ribeauville which was just a smaller, quieter version of Colmar but just as beautiful. 

Such a beautiful. dreamy slice of this world.

anonymous asked:

43 :))

I’m not sure if you wanted angst for this, if so, I’m sorry :( But I hope you enjoy! It’s not my best but I was stuck on how to do this lol. So, sorry.


Antonio and Sylvie haven’t spent much time together lately and he really missed his girlfriend. Although the hours were less at the state attorney’s office, it was still hard to adjust to running his own crew. But tonight he just wanted this night to be about him and Sylvie, nothing else. She at least deserved that.

However, she didn’t know his plans for the night. As much as he would have loved to take Sylvie out on a date, he was in his selfish moods where he just wanted her all to himself. So, he didn’t tell her that he was coming over.

It was around 5 PM when he left his apartment and he got inside his truck. He started his truck and then he pulled away, heading to her apartment. After about 20 minutes, he parked and he shut off his truck. He stepped out, walking up to her apartment. He hoped that she was home, but he figured she was since if she was planning on having girls night, she would have told him.

Antonio walked up to her door and he knocked on it. He smiled when she opened the door a few minutes later. “Hey there.” He said to her.

Sylvie grinned at her boyfriend as she grabbed his arm, pulling him inside. “I didn’t know you were coming over tonight. I would have dressed more better.” She said which made Antonio looked down and noticed that she was wearing pajamas bottoms and a tank top. He shook his head.

“I wanted it to be a surprise. And besides, it doesn’t matter what you’re wearing.” He said as he pulled her into a hug, feeling like it has been weeks since he last seen her.

After a few minutes, he pulled away and he smiled softly at her. “I missed you so much.” He said as he leaned forward and he gave her a kiss. After a few seconds, he deepened the kiss, moving his hands into her hair.

She pulled away from the kiss, needing air. She smirked at him. “You really did miss me, huh?”

“Hell yes.” He said as he took her hand and walked over to the couch. He sat down and he smiled when she sat next to him.

“Are you hungry? I can cook us something.” She offered, which he shook his head to.

“No, if we get hungry, we can just order in. I really don’t want to do anything tonight but just be close to you.” He admitted.

Sylvie smiled softly at him and she nodded her head. “You’re sweet.” She said as she let go of his hand and leaned against him.

At that moment, Antonio shook his head, laughing. “I’m not sweet.” He rolled his eyes, teasingly.

Sylvie leaned back to looked in his eyes. “To me, you are.”

Antonio smiled, nodding his head. “That’s because you’re my girlfriend. If I was rude to you like I am to everyone else, you would end up leaving me.”

Sylvie laughed, shaking her head. “No, I wouldn’t.”

Antonio looked at her, not buying it. “That’s just because you don’t see how I treat others. If you did, you would change your mind.”

Sylvie shook her head, moving over to his lap, straddling his waist. “No, I wouldn’t. I honestly don’t believe you could treat anyone badly. If you did, you wouldn’t have the respect you have.”

Antonio smirked as he placed his hands on her back. He nodded his head. “Maybe so. But I don’t treat anyone the way I treat you. That’s just because you’re special to me.”

Sylvie grinned as she lifted his shirt. “Special, huh? Keep talking.” She urged him to continue as she lifted his shirt over his head with his help.

Antonio nodded his head, smiling at her. “Oh yeah. I mean not everyone would accept all my flaws.” He said, referring to his ex-wife.

Sylvie shook her head immediately at what he said. She took his face in her hand as she stroked his cheek. “Baby, we all have flaws. God knows I have plenty. And the flaws that you’re talking about isn’t even flaws. You’re the best man I know.”

Antonio looked deeply in her eyes as he nodded his head. They were both silent for a few seconds as they got lost in the moment. After a few seconds, Sylvie removed her hands from her hand and she rested her forehead against his. “I feel like I can’t breathe.” She said, breathlessly.

Antonio pulled away slightly to look at her face. “What’s wrong, baby? Are you getting sick?” He asked, a concerned expression appeared on his face.

Sylvie smiled softly as she shook her head. “You honestly have no clue what you do to me.”

Antonio grinned when it finally clicked on what she meant. “It’s the same thing you do to me.”

“But at least you still can breathe.” Sylvie pointed out.

Antonio took her hand in his and then he placed it over his chest, making her feel his heart beat. “You feel it? It’s beating fast already and we aren’t even making love yet.”

Sylvie smirked, pleased with herself. She squealed in delight when Antonio picked her and carried her to her bedroom. “Ah!” She giggled happily.

anonymous asked:


Wow dang that’s a long time, but I suppose if you combine the painfully long HCs post with the 10+ comics, it does add up ^ ^; I’m glad you liked it! :D It’s definitely my biggest baby in the SW fandom ^ ^ It’s currently also on hiatus, I’m in a different fandom now, but I’ll probably go back to it eventually ^ ^;

I had a long caption for this but it deleted.

This is Mariana. She’s 6 (turning 7 soon) and I’m in the long process of adopting her. I decided I wanted to change my life and I am getting a better outcome than I thought I could. I finally got to FaceTime for the first time this tour and we spent hours talking and for the first time in awhile, I’m really happy because things are looking hella good.

I’m so incredibly overwhelmed. Not stressed, really, just….. ugh. Exhausted by life.

I spent over an hour - with the call records to prove it - on the phone with CVS specialty trying to get my progesterone. They changed systems and claimed they “lost” me in the system. Then they said my prescription got deleted because I hadn’t refilled it (um it has 3 refills left). THEN they said the only way to fill it was to get my doctor to fax a NEW prescription, which then got stuck in billing (insurance).

At that point, I had to go to another meeting. I ate my lunch while on a call, then had two back to back meetings.

I came up for air at 4 and spent another 30 mins sitting on hold, when the woman came back and said they’d make an exception and transfer my old prescription to the new system. Oh! So I wasn’t “lost”- you just didn’t want to try. Cool.

But she’d have to call me back and actually arrange the shipment - at some point between 5-7:30 pm. When I was supposed to be in yoga.

I drove to yoga figuring I’d have to keep my phone on my mat and run out if it started to vibrate but she called me back as I was parking.

Then when I got home we discovered one of our credit cards was compromised. Yay redoing auto payment and all that jazz.

I just need to sleep. I’m so done with today.