Recent content by fishsicles

Yeah, but recall that A = theta/2. The geometric argument from the unit hyperbola actually gives (ln x)/2. Apparently my Unicode ² on the e didn't go through so that's fixed.

So. The area under a curve. This is one of the two defining problems of calculus, and the one that's generally more inclined to haunt the nightmares of undergraduate STEM students. Like its twin, the slope of the tangent line, it's something that very clearly Exists, in an intuitive way, but...

I've not seen it used as definitional before, but I can see how that might be interesting. Takes a lot of underlying assumptions to make it, though. Update should be tonight unless I am stricken with The Sickness again at work today.

Every single piece of Xenoblade party dialogue is a meme and rightly so, but "Dunban, you're embarrassing [fifth party member]" lives in my head rent free.

As the person who brought it up: yeah, if you're playing through with normal amounts of overlevelling, it's probably fine. That said, it's really annoying when it does come up.

Yeah, the differential equations that define the hyperbolic trig functions tend to be much more readily applied to real world scenarios than the exponential function, because of fiddly little things like "constraints". I'd say the "most natural" of these is hyperbolic tangent/the logistic function.

Some courses introduce the exponential function alongside two other related functions, \begin{align}\cosh z = {} & \frac{e^z+e^{-z}}{2}\\ \sinh z = {} & \frac{e^z - e^{-z}}{2}\end{align} but it's not always clear why these are called "hyperbolic cosine" and "hyperbolic sine". Well, buckle up...

Hey, at least you don't have to buy them again on NG+!

I do believe I've finally cracked a no-calculus (barring some Riemann sum manipulation, but no actual evaluation of limits or the like so I'm allowing it) proof of Euler's identity. I'll try and type it up this afternoon after work.

I'll throw another bit of spoilers on that I guess.

I will add the important caveat that the party member AI is... extremely character-dependent in quality. AI Reyn is amazing at all of Reyn's jobs, but AI Shulk is only saved from being the most incompetent AI by the existence of party member 6. [/spoiler]

Yeah, XB1 tends to have you overlevelled if you're doing even an appreciable fraction of the sidequests. That said, I've been playing through DE with Expert Mode on, and you end up reasonably underlevelled even hunting down unique monsters, so it's in kind of a strange limbo. Thankfully, level...

You can do gifting in base XB1 and 3D, it's just through the Items menu rather than Affinity.

While there's a lot of things I could say about some of the armor decisions (adding cosmetic equipment slots is far and away the best change in XB1DE), I'll just reference the one funny thing (spoiler is solely mechanical, for Chapter 5):

I presume you mean Ratatouille-style, but my brain leapt to Skaven. take man-thing's ether crystals yes-yes