Recent content by Beamsbox

Part of a chapter review problem. Say you have a sphere centered at the origin and of radius 'a'. And you have a (ice-cream) cone which has it's point at the origin and phi equal to ∏/3. How do I find the equation of their intersection? Which is the projection onto the xy plane...

This guy has some good examples and explanations on multivariable limits:

That's exactly it. It's much easier to prove that it doesn't exist than to prove that it does. Say you prove it doesn't exist just once... well then, it doesn't exist. And yes, you could show it exists for 5 or 6 paths, knowing that you haven't tested them all... and the general consensus would...

Technically speaking, you're never done. That's because you have to prove that the limit exists approaching 0 for every path. We obviously can't prove EVERY path, because there's an infinite amount of paths approaching (0,0) from every direction. So we basically accept that the limit exists once...

Edited to make images easier to see. (Sorry.)

Homework Statement This is a problem form my calculus book, which states: According to the ideal gas law, the pressure, temperature, and volume of a confined gas are related by P=kT/V, where K is a constant. Use differentials to approximate the percentage change in pressure if the temperature...

I remember from a problem I did a while back that the integral of e^{t^2} is not the way to go. Here's my attempt at using the Liebnitz formula, but my answer is quite different, so perhaps I'm not using it correctly... \frac{d}{dx}\int_{1}^{xy} e^{t^2}dt= \frac{d(xy)}{dx}f(x,xy) -...

Homework Statement Stumped. Integral: f(x,y) = ∫ (from 1 to xy) of e^(t^2)dt find both fx and fy The Attempt at a Solution I've come up with: fx(x,y) = ∂/∂x ∫ (from 1 to xy) of e^(t^2)dt Not sure where to go... possibly take the integral, the take the partial derivative? I...

Assignment problem. I have a new issue regarding visualizing graphs of multiple variables. How do you visualize the two of these: f(x,y)=yln(1+x) f(x,y)=sin-1(xy) These completely baffle me. I can see z=ln(1+x), but when you multiply it by y, how does that change it? Does it extend...

Thanks for your quick reply. That definitely helped me understand. I was able to answer both parts of the question with your help. The third part says to show that lim along y=x3 does not exist. Now, I figured it to be 1/3, but I think the book is implying that the limit does not exist...

This is an assignment problem I have. Can't seem to figure it out. It has two parts, one to prove that the function approaches 0 where y=mx and and one where the function approaches 0 from y=kx2... f(x,y) = (x3y)/(2x6+y2) I've attempted both parts and get stuck on what seems like the same...

Ah perfect. I understand the circle at every value of z. I don't understand the 'density function' part though. PErhaps that one will come with time. Thank you, jackmell.

I have a question in my book that states: "T or F The natural domain of f(x,y,z) = sqrt(1-x^2-y^2) is a disk of radius 1 centered at the origin in the xy-plane." This is F as the graph is an infinite solid cylinder. But I can't visualize it. If I let f(x,y,z) be z, and square both sides, I...

Given the following two lines, prove that they are parallel, then find the distance between them... (I have circled in red the two parts of the answer which I don't understand. Namely, why are they using the cross-product here, doesn't that give you a value perpendicular to the lines, hence...

Right, nice assumption, edited and fixed. Long division, I knew I needed it in the form ofthe definition of e, but didn't know how... I'll check it out. Thanks for the help.