#math examples

[math-imagines]

Black Doom Shows You How to Do Integration by Substitution

Gender Neutral Reader, Black Doom & Reader or Black Doom/Reader, up to interpretation

Being in space, you would have assumed that you wouldn’t have to worry about things like math and calculus. It wasn’t like you assumed it wouldn’t be involved in space travel, but you assumed that you wouldn’t have to deal with it with this exact space trip, considering you were abducted by aliens and all. You’d assumed that you were going to be eaten, like everyone else who’d been captured. Yet you and a very small number of others hadn’t yet and were instead being put through a number of tests. A few were physical in some way, but most had tested your intelligence. You couldn’t help but feel like a rat in a maze, being tested on how fast we could change our behavior after being electrocuted. Were these aliens, the Black Arms as you now knew they were called, studying you? If they were, then what for?

This specific test was a test of your ability to do calculations. Vaguely you thought back on that comic that was rather popular a while ago, about someone being forced to do algebraic equations to get into heaven, and couldn’t help but feel that this was something like that. The first few questions weren’t too hard for you, you’d never been bad at math. But when you got into the calculus section, you started to get nervous. You’d only learned so much calculus before you’d been, well, abducted by aliens. And one part in particular always go to you. Integrals in general just hadn’t clicked with you yet. You knew how to do it, but you couldn’t always do it right. It didn’t help that the massive ruler of the Black Arms, Black Doom, was watching everyone testing. You were sure it couldn’t be, but it was almost like he was watching you more than the others.

The next question was about just one of these. Of course it was. It asked what the indefinite integral was of the cube root of seven minus tangent t, all multiplied by secant squared of t. Nothing seemed to be going your way. Why did they even to know if you could do integrals anyway? Surely, they were just going to eat you in the end anyway! Why did they need you to work alone too? Wouldn’t this test be just as effective if you could all work together? You tried to solve the problem anyway, if you only could get a little help…

The floating Black Doom started to move through the space, and to your horror, he came towards you! Had you displeased him in some way? You were quite certain this was when you would be eaten, when he said in his low voice, “You struggle. Why do you persist?”

You glanced around, hoping there would be someone else nearby to respond, but no one did, so you answered nervously, “I don’t know how to do this bit. I hadn’t learned it in class yet. I think I can get it though, if someone…” You paused for a moment, considering whether or not this was a test too. Should you say it? Was that against the rules? No one else spoke, and some others clearly struggled too.

He seemed to read your mind as he let out a low laugh. “It is no shame to require assistance,” he said, “The Black Arms are a hive mind, there is a constant cooperation and collaboration between us. I’ve not seen one of your kind request assistance, not in a non-life threating situation. It takes intelligence to be capable of learning and wisdom to be willing to ask questions. Certainly, you are a promising candidate. Come with me, I will show you how to solve problems such as these.”

…what? Black Doom, ruler of the Black Arms, probably a demi-god, destroyer of worlds, was offering to teach you how to do calculus? Called you intelligent and wise? This couldn’t be real. Shakely, you stood and followed the towering alien out of the room. You still weren’t sure you weren’t going to be eaten, but you followed obediently. And how did he know what you were going to ask for help? Could he read your mind?

“Yes,” he said, though you hadn’t spoken a word. You walked with him down a long corridor now. “We’ve partially attuned you and your fellows to the hive mind. You cannot connect to it, but we can examine your thought processes through it. We use it to determine how well you complete the tests to reveal which of you are most suitable.”

“How are you able to do that?” you asked, knowing there’s no point in leaving it unsaid now. You tried not to think about what “suitable” referred to.

“It’s in your food. A psychokinetically active additive makes your small minds more open to us. We need you all alive for now, so you must eat to live.”

“So, it’s like the radioactive compounds in PET scans, but to see our thoughts instead of our brains?”

He glanced at you, giving a judgmental gaze. “They do not have those in the rest of the civilized universe. Most do not put radioactive compounds in their bodies willingly.”

“Oh.” You walked in silence down the long corridor, until you followed him into an antechamber with a giant tablelike structure in the center.

“I will show you how to complete problems like these,” he declared, moving to one side of the table and indicating that you should join him by scaling a massive seat that seemed more like a monolith than a chair. You managed, with a reasonable amount of effort to climb on top of it. “Good,” he said as you gazed up at him, “You struggled with this.” You nodded as he indicated the problem in question.

“It simply a matter of substitution,” he said, using a massive claw to etch the problem on the table.

“You must simply replace one part of the integral with a separate variable, making it easier to integrate.”You weren’t quite sure you knew what he meant, but you nodded along as he etched a separate variable, u, into the table.

He continued. “It would be more difficult to integrate the cube root of 7 tangent t than of a single variable, such as u. To integrate with respect to u, you must also transform dt to du.” He then wrote a derivative equation:

“Why would we take the derivative of u?”, you asked, confused at the seemingly irrelevant step.

“Have patience,” Black Doom snapped, then continued, “If you’d not interrupted, I would have been able to inform you that the derivative of u is taken to isolate du and dt, and their equivalent portions of the equations.” As he took the derivative of 7 minus 7 tangent t, it made more sense; the majority of the derivative was the factor outside of the radical.

“Multiplying both sides by dt isolates du and dt, making it possible to replace secant squared t and dt with an equivalent expression in that makes the integral possible to integrate in terms of u rather than t.”

When he lay it out before you, it seemed far simpler than you thought it would be. “So, you can take a simpler integral rather than a more complicated one by replacing parts of it with equivalent and simpler variables?”

“Correct,” If Black Doom had a mouth, you could have sworn smiled at you. “Your species’ capacity to learn so rapidly is something we valued in you. If I were to name a positive characteristic in your inferior species, it would be that.”

You gave a weak smile in response, somewhat concerned by his phrasing. You watched him write the edited integral.

This integral was far more reasonable to deal with, a simple matter really. You etched the integrated solution on the table in your smaller hand writing with your writing utensil, something between a pencil and marker.

Black Doom nodded approvingly. “There is but one more step,” he said, “to replace u with what it was originally substituted for.”

“That’s the solution then?” you confirmed.

“Indeed,” he replied. “You are certainly a most suitable candidate. Very adaptable and obedient. I shall keep you in mind for later. Now return to your fellows. Do not bother with completing more of this test, your progress has been deemed satisfactory.”

You nodded and rushed towards the exit, then paused for a moment. “Thank you,” you said, trying not to make your voice shake.

Black Doom looked at you curiously for a moment, after which he said, “As you should. Now begone!”

As you turned and returned to the first chamber you were in, you gave the test you’d completed in a pile of other completed tests and returned to a group of your fellow abductees.

“Oh my chaos!” one gasped as you returned, “You’re alive! We thought for sure you got eaten!”

You shook your head. “No,” you said, “Actually, Black Doom explained calculus to me.”

“You’re clowning? You’re not clowning? I sense clowns.”

“No, I’m serious.” You turned away. “I think there’s something more going on here, though,” you whispered, “I’ve told you before I think they’re studying us, right?”

The others nodded, and some of the Black Arms nearby almost imperceptibly tensed, shifting.

You glanced around, “I think these tests are for more than just study,” you said softly, “I think there’s a bigger goal here. We’re candidates for something. These are just the preliminary tests to determine which of us is best for the real experiment.”

The rest of the group recoiled. “Surely not?” one chuckled nervously. “I mean, the aliens wouldn’t have told you their real plan, right?”

You opened your mouth to double down, but one of the Black Arms jerked their head and reached for a phaser at the edge of your vision. “You’re probably right,” you said, keeping your eye on the alien, “just a theory.”

The group visibly relaxed and so did the surrounding Black Arms. You didn’t though. What had happened still didn’t feel real to you. But as much as you knew something else was going on, you pushed it to the back of your mind, in a place you hoped the Black Arms couldn’t find.

***

Author's Note: Hope you enjoyed and/or learned some calculus from this! Again, if you have any character requests for any fandom or any math topic, just ask. I feel completely deranged for writing this, but I sure did review that topic! I think the plot's not terrible either. Until next time!

[er-cryptid]

Applying Rolle's Theorem with Trigonometry [Ex. 1]

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[wicked-ghoul]

I'm doing sketch commissions through Ko-fi!

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If you're unable to pay for a commission, even a $1 donation to my Ko-fi would be hugely appreciated as I could definitely use the money.

Thanks!!!

~WickedGhoul

[infiniteorangethethird]

not smart as in intelligent but smart as in "people use my above average skills in math to deny me support in every other area of life"

[bitchfitch]

I've been using that fatigue tracking app for about a month now, and so far the main benefit has been like, having proof it's not all just in my head you know? The second benefit has been the contextualization. bc like, When you're sick all the time forever it's really easy to lose sight of what normal is.

for me their scale works out to be that 5 is above average, 4 is doing peachy/normal function, 3 is shits sus be careful bc it's going to be rough, 2 is cancel your plans, 1 is not one Ive gotten yet. (first day was a bad data point from not groking how it worked yet) and idk. Ive had four normal level of function days in the last month. Those should be like. the most common not the least. Confirmed crippled by the app™ and what not I guess

[iwillstabyou]

Happy (very belated) number day!

Yes, I know number day was on the 6th of February and it’s not really a thing for most of you guys, but I think you’ll appreciate this.

As a maths nerd, I love dressing up for number day, and as an even bigger inside no. 9 nerd, there was really only one number that I could pick this year…

Yep, I really did it. I dressed up as David from diddle diddle dumpling and carried a shoe around all day. Did people realise that I was dressed up as the number 9? No. Did I give a flying fuck? No.

Very fun, would recommend

[siph-by-induction]

DO YOU ALL WANNA SEE MY PROOF THAT REFLECTION AND STRETCHES ARE COMMUTATIVE CAUSE I PROVED IT ALGEBRAICALLY AND IT WAS SO FUN

if this gets a note i share my little proof :3 it's very short and uncomplicated i promise

[thistledropkick]

So uh... Immediately after Wrestle Kingdom, the big show that brings in both new and lapsed NJPW fans, and Wrestle Dynasty, the AEW crossover show that was intended to bring new overseas fans to NJPW... New Japan management decided to take the only commentary staff member who speaks any Japanese at all off commentary for two months? So the only remaining English language commentator will just not have any clue what anybody is saying during the entire show? Right when a large influx of new English speaking fans is expected? And they're doing all this just as Kidani, who owns NJPW's parent company, was complaining to Tokyo Sports about how NJPW isn't getting enough overseas fans? Have I got that right?

[khepiari]

Just say that you lack creativity and are jealous of people who can express themselves with their chosen medium of expression. There are millions of ways and tools to express oneself, yet you chose AI to do your hard work, which is “the act of creating”. Feel ashamed, not proud.

[chongoblog]

hey Goofy Math Soviet, what is calculus?

legit, it wasn't necessary for graduation at my school so i never took the class

Basically, it deals with integrals and derivatives, which is tough to explain but I can try.

Remember in earlier math you learned about slope? You know, y=mx + b? If you don’t recall, a slope is basically how steep a line is. Now if you’re looking at a straight line, then it’s pretty easy to determine the slope. Just look at how steep the line in question is and boom. There ya go.

For example take this red line up here. Every time it moves to the right by 1, it moves up 2 and vice versa. So this line has a slope of 2. Simple, right?

But what if we have a line that isn’t as straightforward? Like this curvy boy down here

What’s the slope of this line? A little tougher because how steep the line is different depending on where you are on the line.

That’s where derivatives come in. A Derivative will tell you what the slope of a line is at a given point in time. For example, at the dead center of the graph, the curvy boy has a slope of zero (since it’s flat right there). Once it hits the first square to the right it’s already reached a slope of 2. And at the second square, it’s reached a slope of 4!

How do I know this? Well because I have played you! The red line we looked at earlier is actually a graph of the derivative for the curvy line! So you can use that one to determine how steep the curve is at any given point! So like at -2, the slope is -4, etc.

Integrals are simiar, but in reverse, where you take a look at a derivative and draw out what the original would look like.

I’m being super reductive right now for obvious reasons but thats the bread and butter of calculus. You can do some really really wacky things especially with integrals and as you get further into calculus you use detivatives and integrals to do some dark magic. It’s pretty neat.

Hope this helped!

[er-cryptid]

Derivatives of Hyperbolic Functions [Ex. 2]

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[lotusishere]

I HATE STATISTICS! I HATE IT! I HATE IT! I CAN’T DO IT ANYMORE!!! IF I SEE ANOTHER HW QUESTION ASKING ME “How do you calculate the correlation r?” I’M GOING TO COMMIT SEWERSLIDE! DO I LOOK LIKE I KNOW HOW TO CALCUATE THAT?! NO.

Like what the fuck is this?!

[olive-nothere]

Correct me if I’m wrong because at the end of the day I did fail math and I’m still a rookie when it comes to F1 BUT there’s two things that have crossed my mind and I fail to see people mention when it comes to the whole argument about how a lot of people think Oscar should just have let Lando switch places with him in Monza because “Lando has more of a chance to win the championship” and those things are:

1) Oscar is still in contention (even though yes it will be much harder for him to achieve than if he was in Lando’s position); and

2) even though F1 is a team sport, it’s also a individual sport and Oscar is not going to sacrifice his chances to at least be vice champion just because Lando has more points as of now and specially since he still has a chance to actually win the championship.

Like call me a dumbass or whatever but if I was in Oscar’s place I wouldn’t just give it up if I was still in contention. Not to mention that nothing is set in stone yet so. Oh well anyways would love someone who’s more knowledgeable to correct me if I’m wrong lmao

[cherrymothwaves]

I feel like fandom culture needs to put more value on friendship than it does. I love shipping just as much as the next person, and there are plenty of pairings that I’m obsessed with—but way too many of us treat friendship like it’s a much less valuable connection than romance, and that is just not true at all. Friends can be your family. Family is significant and it will never not be. People always say „they’re just friends.“ and what do you mean JUST!!!!! THAT IS STILL AMAZING. IT IS STILL LOVE. PLEASE RECOGNIZE PLATONIC LOVE YOU GUYS

[meganegatari]

im so obsessed with medical dramas and constantly read about conditions and treatments and operations and assessment methods etc etc etc, my google thinks im a doctor LMAOOO

[thefallenangel2008]

"Oh, I would rather be homeless than do sex work" ok, good for you, but don't be a dick to people who would rather have a roof over their heads and not worry about when they're gonna have their next meal.