@copper.hat I got two responses to my original post. One was yours and I believe I am doing it the way you suggested. The other approach was over my head. I did not understand it.
@robjohn No as in, my point was, when we used feynmans trick we ended up with $f"(t)=4f(t) + (divergent)$, What I was asking was what exactly is the problem in the original integral f(t) which renders feynmans trick unusable? something along the lines of non differentiability or something..
What notation is used more often when introducing a new function, or what would be considered more "natural"?: (1) Define f: D\to R as f(x)=... or (2) Define f: D\to R as x\mapsto ...
English is weird about that. i would never call a box a vessel although the reasoning somewhat holds up. in the context of containers (and not ships) it is usually used for things that hold liquid. i may be wrong about that.
@robjohn Glad to see that at least one moderator, namely you, hasn't abandoned interactions with users. That's a complement! And @Ted, I pretty much place you as a moderator too, so kudos to you, as well, for your dedication here!
@leslietownes What book is that? I know Ted has written a bunch of things, but I haven't been here often enough to know of them all.
it was asking the vector tangent to the curve of steepest ascent on the hill at $(\mathbf{a},c)$. You gave the gradient as $Df(a) = (3,-4)$, so the gradient being normal to my curve means that a taagent vector would be a 90 degree rotation. I used $(4,3)$....in your solution you actually stated it in 3 dimensions: $(3,-4,25)$ wondering if this is a typo? Well part of it seems to be, but where did the 25 come from?
wow...I went through a myriad of looking at things in overly complex forms to just return to the simple notion of "what "rise" value do I need to satisfy the equation slope = rise/run............smh.....getting better at it, but need to chill more on jumping straight to sophisticated things..
also I realize why my tangent vector is wrong....you asked for the tangent vector to the curve of steepest ascent.....not the tangent vector to the level set.........couple sips of yerba mate helped me see the way.
