?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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