Recent content by ohlala191785

Problem: If c is in Vn, show that the function f given by f(x) = c.x (c dot x, where both c and x are vectors) is continuous on ℝn. How do I go about proving this? I'm not sure if c is supposed to be a constant or a constant vector, but since it is bolded in the book I am assuming it is a...

Oh OK. Thank you for your help.

So the description of the surface just an ellipse? If you project the circle onto the slanted plane, it should look like an ellipse.

Homework Statement Consider the surface parameterized by (v cos(u), v sin(u), 45 v cos(u)), where u and v both vary from 0 to 2∏.Homework Equations (v cos(u), v sin(u), 45 v cos(u)) I think this is supposed to be a vector function? As in r(u,v) = <v cos(u), v sin(u), 45 v cos(u)>.The Attempt at...

Thanks for the advice everyone!

Homework Statement Find the volume of the solid that the cylinder r = acosθ cuts out of the sphere of radius a centered at the origin.Homework Equations Cylindrical coordinates: x = rcosθ, y = rsinθ, z=z, r2 = x2+y2, tanθ = y/xThe Attempt at a Solution So I know that the equation for the sphere...

Alright then. Thank you!

So since the min of sin(pi*x) is 0 and max is sqrt(2)/2, and it's the same for cos(pi*x), then the min of their product is 0 and max is 0.5. Is that correct?

k=0.5 I graphed sin∏xcos∏y on Mathematica and saw that for x in [0,1/4] and y in [1/4,1/2], z is between 0 and 0.5. And solving for k=0.5 agrees with the graph. I'm also wondering if you can know that z is from [0,0.5] without graphing it on a computer or something?

Wait hold on is it ∫∫kdA = 1/32, for R = [0,1/4]x[1/4,1/2]? So k(1/4-0)(1/2-1/4)=1/32.

Ohh is it (1/32)(1/4-0)(1/2-1/4)?

k=1/32. Sorry, I still don't know how to proceed.

Homework Statement Using ∫∫kdA = k(b-a)(d-c), where f is a constant function f(x,y) = k and R = [a,b]x[c,d], show that 0 ≤ ∫∫sin∏xcos∏ydA ≤ 1/32, where R = [0,1/4]x[1/4,1/2]. Homework Equations ∫∫kdA = k(b-a)(d-c) 0 ≤ ∫∫sin∏xcos∏ydA ≤ 1/32 The Attempt at a Solution I tried to...

OK I will try plotting. Thanks for the help.

So z is from 0 to 10x^2 + 4y^2, y from 14 to 2x, but what would the limit of x be? The lower bound is 0, how would I find the higher one? Also is the integrand just 1? Thanks!