Jacobian of the transformation T:x=u, y=uv

[karush]

View attachment 8171

how do you graph this in Desmos ?

Assume the rest of the calculation is correct

much thank you ahead...

 

[HOI]

Do you mean how to use Desmos to graph u= 1, u= 2, uv= 1, and uv= 2?

First, of course, Desmos graphs either y= f(x) or x= g(y) so you have to replace u with x and v with y and solve xy= 1 and xy= 2 for y (or x). that is, enter the functions x= 1, x= 2, y= 1/x, and y= 2/x. I limited the axes to that x and y were between 0 and 3 to get a good graph.

 

[karush]

Do you mean how to use Desmos to graph u= 1, u= 2, uv= 1, and uv= 2?

First, of course, Desmos graphs either y= f(x) or x= g(y) so you have to replace u with x and v with y and solve xy= 1 and xy= 2 for y (or x). that is, enter the functions x= 1, x= 2, y= 1/x, and y= 2/x. I limited the axes to that x and y were between 0 and 3 to get a good graph.

View attachment 8176

ok here is my eventual typeset

desmos plot is here

https://www.desmos.com/calculator/cmqpsbp85y