# Where should I start?

1. Sep 22, 2010

### atomicpedals

I've been working at this problem off and on all day (I come back to it after finishing others hoping I'll get a great idea)... I still have no clue how I should even start. Any hints in the right direction would be most welcome. So, without further ado, here's the question:

Show that the square R(xy):0.9 $$\leq$$ x $$\leq$$ 1.1, -0.1$$\leq$$ y $$\leq$$ 0.1 corresponds to the region R(uv) bounded by arcs of the circles u^2+v^2=e^1.8, u^2+v^2=e^2.2 and the rays v= +/-(tan 0.1)u, u$$\geq$$ 0, and find the ratio of the area of R(uv) to that of R(xy).

If I'm reading the problem correctly it's essentially a mapping. And I'm pretty sure that a Jacobian determinant will be involved in some way. Do I construct a Jacobian from the forms of R(xy) and R(uv)? But how does that get me the requested ratio?

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