Recent content by namu

Homework Statement Consider the surface defined by F(x,y,z)=1/2(x+y)^2+(y+z)^2+(x+z)^2=9 (a) Evaluate grad(F) My Solution: grad(F)=(3x+y+2z, x+3y+2z, 2x+2y+4z) (b) Find the highest and lowest points on the surface (i.e. the points where z attains a maximum or minimum). Problem: So I...

What is ##p'(x)##? It is \lim_{h \to 0} \frac{p(x+h)-p(x)}{h} Hence, p(x)+hp'(x)=p(x+h) So now we have \lim_{h\to 0}\frac{F(p(x+h))-F(p(x))}{h}=F'(p(x))=p'(x)f(p(x))

Ok, round 2, here it goes. 4u^2=4x^2 y^2 v^2=x^4-2x^2y^2+y^4 4u^2+v^2=x^4+2x^2 y^2+y^4=(x^2+y^2)^2=\rho^2 Thank you!

Sorry, I made a typo since I was copy pasting 4u^2=4x^2 y^2

Im still lost. I want \rho=x^2+y^2. 4u^2=x^2+y^2 v^2=x^4-2x^2y^2+y^4 I'm still getting nowhere.

you can take the derivative which gives you the rate of change. Then, if you want to integrate from say starting from the origin, evaluate the derivatives at zero, and the greater of the two would be on top. If you have something like f=x^2 & g=x^4, then f'=2x & g'=4x^3. At the origin, they both...

Homework Statement Find the mass of the plane region R in the first quadrant of the (x,y)-plane bounded by the hyperbolas xy=1 \,\,\,\,\,\,\,\,\,\, xy=2\,\,\,\,\,\,\,\,\,\, x^2-y^2=3\,\,\,\,\,\,\,\,\,\, x^2-y^2=5 Assume the density at the point (x,y) is \rho=x^2+y^2 Homework...

usually general prob, physics, and chem ?'s appear. For example, see http://chemgradschool.blogspot.com/2009/02/shortly-after-submitting-my-application.html Thank you!

I worked it out and I got the correct answer. Thank you!

That was what I was originally thinking, however I am studying for an exam, and there have been other similar questions to reflect a curve or another surface about the plane. Then I am not so sure what to do.

OK, let me first give the change of coordinates a try. I want x'=15 , so let y'=-z z'=z x'=x So the plane x+2*y+2*z=15 becomes x'=15 and the sphere (x-2)^2+(y-1)^2+(z-1)^2=4 becomes (x'-2)^2+(z'+1)^2+(z'-1)^2=4 . That's a weird equation for a sphere, but I take its...

Hello everyone, I have luckily gotten into the first round of the Hertz fellowship interview. Does anyone have any suggesitons that would help me to prepare? Are there any past Hertz fellows or others who have gotten into the interview? If so, can you guys drill me with similar...

Homework Statement Given the sphere (x-2)^2+(y-1)^2+(z-1)^2=4 and the plane x+2*y+2*z=15, find the equation of that sphere which is the mirror image of the given sphere relative to the given plane. The Attempt at a Solution I was thinking the following constraint #1: eq. of...

Yes, silly mistake. I fixed it. See above. Thank you.

Yes, that is exactly it. It is \frac{e^b-1-b}{b} Thank you.