Recent content by grog

ah. that's what it was. I forgot about the formula for area. : ( Thanks!

Homework Statement Find the area enclosed inside r=3 sin (theta) Homework Equations integral?The Attempt at a Solution basically, I took \int3sin\Theta from 0 to 2pi, then pulled the 3 out to get 3\int sin\Theta from 0 to 2pi and then 3[-cos(\Theta)] evaluated from 0 to 2pi. that seems...

ok, so it looks like I got my approach wrong. The way it's worked out it looks like the e distributes to the other term, and then I should differentiate, which yields e-x^2-y^2*2x =- 2x^3*e-x^2-y^2 and e-x^2-y^2 * 4y-4y^3e-x^2-y^2 which reduces to 2x(1-x^2) = 0 4y(1-y^2) = 0...

ah. ok. so I should have ended up with fx= x2+2y2 -1 = 0 and fy=x2+2y2-2 = 0 So to find the critical points I have to solve these two equations. Would I be on the right track to say fxthen simplifies to (x-1)(x+1)+2y2 = 0 If so, I'm embarassed to say I'm still not sure how to...

so I would end up with 4x-2y and zero for the two normal vectors? and then take the cross product of the two? I think I may be confusing some concepts here.

Homework Statement Find the absolute minimum and maximum values of f on the set D. f(x,y)= e-x2-y2(x2+2y2); D is the disk x2+y2 <= 4 Homework Equations Second Derivatives test, partial derivatives The Attempt at a Solution fx(x,y) = 0 = (e-x2-y2)(-2x) + (x2+2y2)(-2x...

Homework Statement Find parametric equations of the tangent line at the point (-2,2,4) to the curve of intersection of the surface z=2x2-y2 and the plane z=4 Homework Equations Not sure The Attempt at a Solution Not sure quite how to approach this. take the gradient of...

ok, based on the solution to another problem, I've worked out: F(x,y,z) = xy+yz+zx = 0 Fx = y+z = 2 Fy = x+z = 2 Fz = y+x = 2 and the equation of the plane as 2(x-1) + 2(y-1) + 2(z-1) = 0 or x+y+z = 3 How does that look for the equation of the tangent plane?

Homework Statement Find the equations of the tangent plane and the normal line to the given surface at the specified point. xy+yz+zx=3 @ (1,1,1) Homework Equations z-z0=fx(x0,y0)(x-x0) + fy(x0,y0)(y-y0) The Attempt at a Solution I feel like this should be really easy, but I'm...

At first it's really tedious, but once you start to get the hang of it, it's not that bad. When you're posting, there is a series of controls at the top of the box. the sigma will bring up a clickable interface so you can choose different symbols, and the subscript and superscript symbols are...

doh! of course. I don't know why I couldn't see it as a u substitution problem. Thanks all for the responses.

Homework Statement Find the length of the curve r(t) = <2t3/2 , cos 2t, sin 2t>, for 0<= t <=1 Homework Equations L = \int\sqrt{(dx/dt)^2+(dy/dt)^2+(dz/dt)^2}dt The Attempt at a Solution (dx/dt)2 = (3t1/2)2 (dy/dt)2 = (-2 sin(2t))2 (dz/dt)2 = (2 cos(2t))2...

Thanks!

The problem doesn't seem to specify. how would I tell, and how would that affect my answer?

Homework Statement The alaskan pipeline has a capacity of 2.37*105m3/day of oil per day. Along most of the pipeline the radius is 60 cm. Find the pressure at a point where the pipe has a 35 cm radius. Take the pressure in the section with radius 60 cm to be 160 kPa and the density of oil...