Rainbow Dash Learns Calculus
A boom. A crash. A muffled voice - "Hey, what gives?"
Glad to have invested in the fibreglass windows, Twilight marked the page of her book and took her time opening the door to the library. "Can I help you?" she sang, smirking.
Shaking her head to clear the pain, Rainbow Dash said "Yeah, I need to borrow some books."
Frowning briefly, Twilight checked her calendar before raising her eyebrows, confused. "The next Daring Do book isn't out until next month. You, of - "
"Yeah, yeah, I know," Rainbow Dash waved off. "But I'm not here for that."
"Then what are you here for?" asked Twilight Sparkle, perplexed.
Fidgeting, tail twitching, Rainbow Dash stammered, "Well... the ponies in Cloudsdale, y'know, the head honchos told me that we actually need to know the dynamics of weather or whatever. Personally, I can control it just fine, but they insisted that I take a course with them this November."
Twilight blinked twice, then smiled. "I'm sure I have quite the number of textbooks on aerodynamics and maybe even a few on meteorology! Lemme see..." She giggled to herself.
Rainbow Dash coughed and said, "That won't be necessary. They'll provide the texts when it's time. But they said that I'm responsible for getting my math skills on par before I take the course."
Raising her eyebrows, Twilight muttered, "Just how far behind are you? And what do you need to learn?"
Rainbow Dash let her eyes wander over the library. "I know high school algebra. And... I need to learn calculus."
"Calculus? Gosh, Rainbow, I don't know if you'll be able to get it done by November. I mean, if we were talking about any other pony..." Twilight was stopped by a glare. She coughed. "Well, if you're sure you're up for learning it by yourself in nine months..."
Rainbow Dash rolled her eyes. "As if I have any choice. Either that, or I get demoted."
Twilight nodded. "Follow me."
With her Stewart, 2nd edition in hoof, Rainbow Dash flew off to her cloud home. She flopped onto her bed, got into her reading position, and made herself comfortable. She opened the textbook, flipped through all the fluff, and got started. "Let f(x) be defined on the closed interval [a,b] that contains c, except possibly at c. Then, we say that lim_x -> c f(x)= L if, for every ε > 0, there exists a δ > 0 such that for x ∈ [a,b], 0 < | x - c | < δ , we have | f(x) - L | < ε."
This was going to be a long nine months.
"Hey, Rainbow! How's the calculus coming along?" Twilight asked enthusiastically. She motioned for Rainbow Dash to take a seat beside her.
Rainbow Dash set her tray down. "Not in public!" she blushed. Whispering, she added, "I think I'm screwed."
Twilight Sparkle smiled. "I sort of anticipated this," she started. "Calculus isn't easy, especially for someone - Ow!" She checked herself, then continued. "If you'd be willing to invest an hour or so every day, then I'd be willing to help you with your studies."
Rainbow Dash brightened up. "Really? That'd be great!" she exclaimed. "The smartest mare in Ponyville is going to teach me calculus!"
Twilight could feel her cheeks turning red. "Oh, I'm not sure if I'm that good..." She finished her daisy sandwich and got up, taking her plate and giving it to Pinkie Pie.
"Nonsense!" Rainbow Dash rebutted. "Today at seven?"
"Sure," Twilight said. "See you then!"
Ten hours later, Twilight heard the door to the library open. She shelved one last book and said, "Welcome to the library! Is there - oh, hey, Rainbow Dash! Ready for calculus?"
Rainbow Dash nodded nervously.
"Great! Let's get started! Ooh, it's been years since I've touched this stuff... I think we start with the concept of a limit, right?"
"Yeah," Rainbow Dash said, fidgeting.
"Great! D'you know what a limit is?"
Rainbow Dash shook her head.
"Well, let f(x) be defined on the closed interval [a,b] that contains c, except possibly at c. Then, we say that the limit as x approaches c of f(x) = L if, for every ε > 0, there exists a δ > 0 such that for x ∈ [a,b], 0 < | x - c | < δ , we have | f(x) - L | < ε. Got that?" Twilight asked.
"Umm, what does that epsilon-delta-whatchamacallit mumbo-jumbo mean?" Rainbow Dash could feel the start of a headache coming on.
"It means exactly what it says!" Twilight said. "What part of it don't you understand?"
"How 'bout let's start with a, b, c, L, epsilon, and delta?"
"They're just variables!" Twilight frowned.
"But how do they vary?!" Rainbow Dash asked.
"That depends on the function!" Twilight said, exasperated. "Look, let's just try an example." She took Rainbow Dash's textbook and flipped to the appropriate page.
"Won't the diagrams help make things clearer?" Rainbow Dash asked, pointing to an image in the textbook.
"Who needs diagrams?!" Twilight rolled her eyes. She pointed to question fifty-two and said, "Try solving this one."
52) lim_x -> 0 ln(x^2 + 1)^2
Rainbow looked at it and groaned. "What am I supposed to do with it?"
"You mean you don't see?"
"Darn right I don't see! What is this supposed to mean?"
"It means you take the limit of it as it approaches zero from both sides!"
"What's a limit!?"
Dear Ms. Dash,
We regret to inform you that due to your failure to participate in our Dynamics of the Atmosphere program, your post as chief meteorologist of Ponyville will be passed on to another weather pegasus who has the requisite education, and you will take on the role of an ordinary cloud clearer, under the direction of Blossomforth, effective next Monday, January 12. Your salary and benefits will be deducted in accordance with this change.
Should you, in the future, take the initiative to educate yourself at an accredited institution (see attached list of acceptable degrees), as we do not foresee offering such a course in the near future, you will be considered for promotion at that time.
Sincerely,
The Cloudsdale Weather Factory
