Recent content by jk8985

How would I make that at the point (0,0,1) [i think it was that point] - - - Updated - - - My apologies for the bad grammar, by the way, I'm on my phone.

This is exactly what I ended up getting, with theta equalling ~1 radian. How would I go about finding the tangent line? I would always think it's a plane, so I didn't know how to approach it.

So I tried this: x^2+y^2-z=-1 and I know the angle=arccos(dot product of normal unit vectors) But I don't know exactly what to do :(

For the second half of the question, I got this. Is it correct?? Also, could you write it out nicely :( I don't really understand what I did. Can someone let me know if this is correct and if I showed all steps? Since the the region of integration inside x^2 + y^2 = 1 (and symmetry), convert...

awesome, exactly what I got when I did it. If you could help me with this, it would be awesome :) http://mathhelpboards.com/calculus-10/angle-between-two-planes-8180.html

The graph of z=x^2+y^2+1 and the graph of x+y+z=e^(xyz) have a common point (0,0,1). Find the angle between the two corresponding tangent planes respect to these two graphs at point (0,0,1). In addition, find the tangent line of the curve intersected by these two graphs at point (0,0,1).

I get a non-real result when doing from 0 to -1 :( for the second double integral. for the first set of double integrals i get 11/30

∫-1(lower limit) to 0 (upper limit) ∫(-1 (lower limit) to y−y^3 (upper limit)) y dxdy plus ∫0 (lower limit) to 1 (upper limit) ∫(√(y)-1)) (lower limit) to (y−y^3) (upper limit) y dxdy I did mine as two different double integrals. Is that okay? Did I get the two sets of double integrals...

Oh wait! I think I got it. Is this the integral? ∫0 to -1 ∫(-1 to y−y^3) y dxdy plus ∫0 to 1 ∫(√(y−1)) to (y−y^3) ydxdy I don't really understand why these are the limits of integration though, and why they are added together.

I think it's a Type 2, but I'm not sure. I have no idea how to approach the limits of integration. Would you be able to provide an explanation on how to do so? It would be awesome :D

Find the double integral of (integral sign) (integral sign) ydA where D is the region bounded by (x+1)^2, x=y-y^3, x=-1, and y=-1

Let E be the solid inside cylinder y^2+z^2=1 and x^2+z^2=1, find the volume of e and the surface area of e