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1. ### Change of variables formula

I got the answer! Thank you!. However, If i wanted to solve it with the integral in dxdy, would i need to use two integrals?
2. ### Change of variables formula

. I Evaluated this and x = 2y-6 and x = 2y - 12 ?
3. ### Change of variables formula

No problem man! I initially tried setting the points I found as the limits of integration but then realized that I couldn't do that. After I plotted the points I found I saw that they formed a rhombus. So I found an equation for x in terms of y and set it up as follows...
4. ### Change of variables formula

Why would I use the change of variables theorem to compute an integral in the xy plane? Sorry if this sounded too demanding but I've been staring at this problem for quite some time now.
5. ### Change of variables formula

Homework Statement Homework Equations N/A The Attempt at a Solution I solved part a. I got an answer of 140. For part b, however, I am stuck. I came up with a set of points for D in the xy plane [(0,3)(0,6)(4,5)(4,8)] giving me a rhombus. How do i integrate this? I tried to split up the...
6. ### Recast a given vector field F in cylindrical coordinates

I don't have my homework with me, but I forgot to edit my post with the answer I got. The ez terms canceled
7. ### Recast a given vector field F in cylindrical coordinates

Hello! Sorry I just saw this reply. As an answer, I got (rcos(θ)sin(θ)er +rcos2(θ)eθ +(2cos(θ)sin(θ)z+ 2sin(θ)cos(θ)z)ez Is this answer correct? Edit- Yes! I figured out my mistake and I got an equivalent answer. Thank you for the help Charles
8. ### Recast a given vector field F in cylindrical coordinates

Homework Statement F(x,y,z) = xzi Homework Equations N/A The Attempt at a Solution I just said that x = rcos(θ) so F(r,θ,z) = rcos(θ)z. Is this correct? Beaucse I am also asked to find curl of F in Cartesian coordinates and compare to curl of F in cylindrical coordinates. For Curl of F in...
9. ### Unit vector perpendicular to the level curve at point

Oh that makes much more sense. Thank you.
10. ### Unit vector perpendicular to the level curve at point

No problem at all. I just wasn't sure what a level curve was.
11. ### Unit vector perpendicular to the level curve at point

Homework Statement Find the unit vector perpendicular to the level curve of f(x,y) = x2y-10xy-9y2 at (2,-1) Homework Equations Gradient The Attempt at a Solution I'm not sure what it's asking. Wouldn't this just be the gradient of f(x,y) evaluated at (2,-1) then normalized? or am I missing...