?In the following exercises, the function \(T: S \rightarrow R, T(u, v)=(x, y)\) on the
Chapter 5, Problem 357(choose chapter or problem)
In the following exercises, the function \(T: S \rightarrow R, T(u, v)=(x, y)\) on the region \(S=\{(u, v) \mid 0 \leq u \leq 1,0 \leq v \leq 1\}\) bounded by the unit square is given, where \(R \subset \mathrm{R}^{2}\) is the image of S under T.
a. Justify that the function T is a \(C^{1}\) transformation.
b. Find the images of the vertices of the unit square S through the function T.
c. Determine the image R of the unit square S and graph it.
\(x=\frac{u}{2}, y=\frac{v}{3}\)
Text Transcription:
T: S rightarrow R, T(u, v)=(x, y)
S={(u, v) | 0 leq u leq 1,0 leq v leq 1}
R subset R^2
C^1
x=u/2, y=v/3
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