Recent content by forty

(6k+1)(6n+1) 6(6kn+k+n)+1 m = (6kn+k+n) is that what you mean?

Show the progression (6k +1) (k is an integer) is closed under multiplication: Firstly I should check that I remember what this means... If it is closed when you multiply any 2 elements together you get an element that is in the set? So for this I thought just show (6k+1)(6n+1), where k...

Thanks for the help. Finally got to the bottom of it with help from a mate. Mark44 you where right I didn't need to do an epsilon-delta proof, simple a LHS = RHS using limit properties and you hinted at! Just so use to seeing epsilon-delta proofs everywhere in real analysis. But in short took...

Mark44 I had a look at the properties and found nothing really useful. And I do think that I had to use an epsilon-delta proof >.< (they get very cumbersome very fast!) hamster143 I don't know where that property comes from and I don't really have any idea how to apply it to the proof. I...

I'm trying to prove that: lim(x->a) e^f(x) = e^lim(x->a)f(x) (Assume lim(x->a)f(x) exists) However I am having great difficulty! My only real approach I have taken is epsilon-delta proof. if \epsilon > 0 then there exists \delta > 0 such that if |x - a| < \delta then | e^f(x) -...

How would I change my parameter so I could rotate it to make it nicer?

Show that the circle that is in the intersection of the plane x+y+z=0 and the sphere x2+y2+z2=1 can be expressed as: x(\vartheta) = (cos(\vartheta)-(3)1/2sin(\vartheta)) / (61/2)y(\vartheta) = (cos(\vartheta)+(3)1/2sin(\vartheta)) / (61/2)z(\vartheta) = -(2cos(\vartheta)) / (61/2) I'm really...

I would use cylindrical coordinates usually but the question says explicitly to use Cartesian. And also doing the integration you suggested I get -16pi. How can the volume be negative? (I always feel so bad questioning you!)

I end up with 64 times the integral from -(pi/2) to (pi/2) of (cos(t))^4 dt. Is this right? *I found the solution to this using trig identities (24pi), but have I ended up with the right integral?*

Find the volume of the region between the two paraboloids z1=2x2+2y2-2 and z2=10-x2-y2 using Cartesian coordinates. I let z1 = z2 and solved this to get the intersection of the two paraboloids which gave y2+x2=4 (Which I can also use as my domain for integration?) So the volume of the area...

Using P2(x,y), find a quadratic approximation to ln(1.25) to 4 decimal places. The original function is f(x,y)=ln(x2 + y2) and is about the point (1,0). I calculated P2 to be y2-x2+4x-3 however I don't know how to find a quadratic approximation. Do I just set say x=1 and y=.5? Any...

Find a pair of fields having equal and divergences in some region, having the same values on the boundary of that region, and yet having different curls. I really have no idea on where to start for this. Would making up 2 arbitrary fields in spherical co-ordinates work? a(theta) + b\phi +...

It's been a long time since I've had to do this stuff so bare with me! Compute and graph the following: (a) -15+i/4+2i (multiply by the conjugate and I got -2.9+1.7i (b) (271/3)4 Now for some reason I have a feeling this has 3 solutions using complex numbers but can not figure them out...

I figured that after the first post I should of put up a picture. Thanks for clearing that up Doc Al (like always :) ). All makes sense now! Thanks all!

Yeah I see that now... but rl.bhat said dE = μο/4π*λ*cosθ*dθ/R. Τake the integration from 0 to π. isnt that integral 0? (isn't the integral of cos(θ)dθ from 0 to pi equal to 0?)