Hi, I'm having a hard time with this:

#48 Consider the change of variables from the xy-plane to the uv-plane given by the equations: u = x^(1/3) + y and v = 1 + y

Under this transformation, the image of the region (x,y): x element of [0,1], y element of [0,1] is which of the shaded regions?

Why is the answer not A?

Thanks

## GRE 9768 Question 48

### Re: GRE 9768 Question 48

sorry i mean why is it not D?

### Re: GRE 9768 Question 48

Consider the square of side one in he xy-plane

parametrize the square:

x=t, y=0 t from 0 to 1

x=1, y=t t from 0 to 1

x=t, y=1 t from 1 to 0

x=0, y=t t from 1 to 0

The orientation doesn't really matter.

In any case sub in the above param. into change

u=t, v=1 t from 0 to 1

u=1+t v=1+t t from 0 to 1

u=t+1, v=2 t from 1 to 0

u=t, v=1+t t from 1 to 0

And that is choice A

parametrize the square:

x=t, y=0 t from 0 to 1

x=1, y=t t from 0 to 1

x=t, y=1 t from 1 to 0

x=0, y=t t from 1 to 0

The orientation doesn't really matter.

In any case sub in the above param. into change

u=t, v=1 t from 0 to 1

u=1+t v=1+t t from 0 to 1

u=t+1, v=2 t from 1 to 0

u=t, v=1+t t from 1 to 0

And that is choice A