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Use a computer to graph the parametric surface. Get a printout and indicate on it which grid curves have $ u $ constant and which have $ v $ constant.

$ \textbf{r}(u, v) = \langle u^2, v^2, u + v \rangle $,

$ -1 \leqslant u \leqslant 1 $, $ -1 \leqslant v \leqslant 1 $

GRAPH

Vector Calculus

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Johns Hopkins University

Oregon State University

Baylor University

Boston College

in this problem, we are given the Parametric surface Ex u V equals u squared. Why a view V equals V squared and Z of UV equals U plus V. So with that in mind, we know that U and V range from negative one toe one so we can plot something like this. Ondas not gonna be perfect. That's OK. It's just a general plot of the graph. We know that it's gonna go positive and negative. So we wanna have thes ranges down here that's gonna go all the way from zero. We use bloom, so it's gonna go from zero upto one. It's gonna be like this sheet. It's gonna come down, Andi, almost like folds on itself like this. And then there's another portion around here that comes down like this and that goes in. And then this final park curves down here. So that's kind of what the shape looks like. Um, as you see here, it's not gonna be perfect. But if you use a computer software, it'll be a lot more accurate and you'll get a better visual of it. So if we keep you constant, um, se call it you not than X is going to be. You're not squared. And then if we keep V Constant, then we'll get if he not squared on Ben the correspondent grid curves are the planes parallel to the X Z plane. Um, if we keep this constant right here, then the corresponding grid curves are planes constant to the Y Z plane.

California Baptist University

Vector Calculus