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Description
I wish I wasn’t stupid at calculus.
Artist description:
For MLP Artist Training Grounds Week 89: “A Pony at Their Limits”.
It’s been a while since I last stayed up at night to submit an image to MLP-ATG Alumni before the deadline. I need to draw more.
And it is now precisely one year since I joined deviantArt! Yay!
Source
I simply used dt instead of Δt because I was too go looking for it. And I also agree with the usage of Δt, however defining t0 would have made sense in my opinion.
^ Yes, this. ^
*correction;
dt = lim t -> 0 t = 0
So, that’s not exactly what I meant, that was incorrect. dt, I should say, means “infinitely small but not zero,” hence we use terms like dx/dt to describe an infinitesimal change in position (x) with an infinitesimal change in time (t), describing the velocity at a single instant in time (Δt = 0).
Specializing in general relativity, though, it’s actually kind of funny that relativists often use “dx” incorrectly as though it were a Δx. It’s not strictly mathematically correct, but it’s just kind of the funny convention that works for most physics applications that’s arisen in the field (when it comes to really manipulating the maths, though, then they serious up and do it right).
To be precise, dt is used to mean “an infentesimally small change in t,” while, at least from what I’ve seen, Δt (though I had to go to open office, insert special character and copy-paste it here to get the little Δ, haha) is more often understood to mean an actual non-limit-approaching-zero interval of time,
Δt = t final - t initial
dt = lim t -> 0 t
Meanwhile, if he’d just used “t” by itself, that would be rather meaningless because t is just a coordinate, without reference to anything else it doesn’t make any sense. Time approaching some arbitrary point we’ve marked as “zero” means nothing. What’s stressful is when your current time, minus the time to the important event
Δt = | t current - t event |
Approaches zero, with the implication that it’s not enough time to do what you need to do in that span of time.
Thus my defense of OP not being a duck; I agree with his choice of using Δt instead of t.
“tl;dr OP is a faggot who didn’t define his variable, thus causing confusion.”
I agree. Twilight is badly defined
I think that would depend on how you define t. Assuming that t represents the current time, dt represents the difference between the current time and, likely, the set latest time for completion of the task at hand. Thus, dt->0 means that the function approaches the set ultimatum. In this case, t->0 would be impractical, since it would represent the beginning of time. However, if you define t as the time remaining to the ultimatum, then t->0 would indeed make more sense.
tl;dr OP is a faggot who didn’t define his variable, thus causing confusion.
maybe delta t is defined as the time between now and the deadline for her friendship report