Recent content by dr721

Have to declare my major this year and I'm stuck between a rock and a hard place. I was previously a physics major, but decided to change tracks due to my stronger interest in chemistry, biology, and engineering. My current plans are to try to go to medical school and get into academic...

Nevermind, I just thought about that v, -v statement. Thanks voko!

Yes, it is my question, and it is also copied verbatim from our book. And this question is not listed under the list of errors for the book, so I'm sorry if it seems wrong, but I have a strong feeling knowing my professor (who authored the book) that it is indeed accurate.

Right, so that'd be D and -D as -v is multiplied by the scalar -1. Would it be possible for somebody to restate the question? I'm not sure I understand what it's asking.

Homework Statement There exists no function f: ℝn \rightarrow ℝ so that for some point a \in ℝn, we have Dvf(a) > 0 for all nonzero vectors v \in ℝn. 2. The attempt at a solution No quite sure where to go with this one, any help would be great!

Actually, I don't know that specific definition at all. My calculus teacher spent very little time doing limits. We learned the basic skill of taking a limit and L'Hopital's Rule, and then went straight into derivatives. I know a limit is a way of looking at the continuity/discontinuity of a...

I guess I don't actually understand what epsilon and delta mean. Like, I'm struggling to understand how they define the limit.

Homework Statement (Squeeze Principle) Suppose f, g, and h are real-valued functions on a neighborhood of a (perhaps not including the point a itself). Suppose f(x) ≤ g(x) ≤ h(x) for all x and limx→a f(x) = l = limx→a h(x). Prove that limx→a g(x) = l. (Hint: Given ε > 0, show that there is δ...

Sorry for the poor formatting. I don't know how to format column vectors or fractions.

Homework Statement Consider the surface z = f\left(x y\right) = xy. Given a point P = \left[a, b, ab\right] on this surface, show that the lines with direction vectors u = \left[1, 0, b\right] and v = \left[0, 1, a\right] through P are entirely contained in the surface. 2. The attempt at...

Right, I can see the formula as being true. My fear was that as he had yet to introduce it in class, my professor may frown upon its use. That said, I'm a bit confused about this idea of creating another vector in that same plane and using it to solve for x. I don't see how the formulas allow...

Well, that formula appears nowhere in my notes, memory, or book up to this point. So I would assume he wants us to be able to solve the problem without it. Would that be possible? Otherwise, crossing a with c would give me a vector y that lies in the a, x span. But then how are you applying the...

Yes, it would stand to reason that you would know that point. And no, we have yet to learn such a formula.

Well, it would be a vector perpendicular to its cross product. And, I suppose it would be a linear combination of the vector a. I know a lot of tedious algebra might describe it, but I guess I don't really know how I would describe a picture per se. I don't know how I would break it down to...

Homework Statement Given the nonzero vector a ε ℝ3, a\dot{}x = b ε ℝ, and a × x = c ε ℝ3, can you determine the vector x ε ℝ3? If so, give a geometric construction for x. Homework Equations a\dot{}x = ||a||||x||cos\Theta The Attempt at a Solution I'm not really certain what it is...