Fair enough!
Hence the tangent plane is
Well that was nice! The rest of the question is tricky though!
This is where I start to have trouble.
The answer I have so far is
,
and
.
Where
and
and
are the new x,y and z values respectively.
I've been trying to get
in terms of
and
, but I can't elminate t!
Call the tangent plane
.
Hence
.
This is where I start to get a little confused. I was hoping to set
to 0 since the x-y plane has a gradient of 0. However,
is a constant function so can never equal 0!
The problem here is that I appear to have three variables:
and
. This seems to contradict the fact that this is a double integral.
Is z a variable or a constant? If z is a variable then is
?
I would appreciate on any of the parts to this question.
If you have any ideas or explanations to any parts, feel free to post!!