jb_nc
Google "9-11" and "truth"
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Ok, I didn't know where to post this but there is one question to do with Ex 2 I've forgotten how to do (for mah test on Monday). There isn't really a uni maths help subforum that gets posted in more than once a month. So uni people any help would be appreciated because I have nfi. I mean I even typed them up in LaTex.
1) Sketch the region
of the complex plane. abs(x) means absolute value/modulus just fyi. lol @ not being able to do it, i know. i never paid attention in inequalities.
[This is pretty hard AFAIK, last question in a test] 2) The equation
defines a curve in the (x,y)-plane through the point (1,1). Find the tangent to this curve at (1,1).
3) i) [Can do this part just runs onto ii)] Using L'Hôpital's rule, show that![](/proxy.php?image=http%3A%2F%2Fimg293.imageshack.us%2Fimg293%2F8186%2Flimitonenewsv0.png&hash=a26283f131b7c6a62db4be216d72cd6f)
ii) Hence find
.
4) An ant walks on the surface z = 9x2 + 4y2 + 6xy in such a way that its position at time t is determined by the parametric equations:
x(t) = 2cos(t) and y(t) = 3sin(t) for t≥0.
i) [If someone could prove this using the partial derivative chain rule that would be great] Use the Chain Rule to show dz/dt = 36cost(2t)
ii) Hence, find the first time t > 0 that the ant is at its maximum heigh above the xy-plane as it walks on the surface z = 9x2 + 4y2 + 6xy.
Cheers.
1) Sketch the region
![](/proxy.php?image=http%3A%2F%2Fimg201.imageshack.us%2Fimg201%2F7050%2Fcomplexoi0.png&hash=4698ef3eacefcf2dd6555e8063872b82)
[This is pretty hard AFAIK, last question in a test] 2) The equation
![](/proxy.php?image=http%3A%2F%2Fimg201.imageshack.us%2Fimg201%2F6905%2Ftangenteq6.png&hash=f07802a677de40ba6887f1e17a26f727)
3) i) [Can do this part just runs onto ii)] Using L'Hôpital's rule, show that
![](/proxy.php?image=http%3A%2F%2Fimg293.imageshack.us%2Fimg293%2F8186%2Flimitonenewsv0.png&hash=a26283f131b7c6a62db4be216d72cd6f)
ii) Hence find
![](/proxy.php?image=http%3A%2F%2Fimg300.imageshack.us%2Fimg300%2F7937%2Fsecondlimitlb8.png&hash=63e17439286b68def9186b198e61275e)
4) An ant walks on the surface z = 9x2 + 4y2 + 6xy in such a way that its position at time t is determined by the parametric equations:
x(t) = 2cos(t) and y(t) = 3sin(t) for t≥0.
i) [If someone could prove this using the partial derivative chain rule that would be great] Use the Chain Rule to show dz/dt = 36cost(2t)
ii) Hence, find the first time t > 0 that the ant is at its maximum heigh above the xy-plane as it walks on the surface z = 9x2 + 4y2 + 6xy.
Cheers.
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