Solve for #1 ### Problem 3**Objective:** Find the image R in the xy-plane of the region S using the given transformation T. Sketch both R and S.**Given Data:**1. For \( S = \{ (u,v) : 1 \leq u \leq 3, 2 \leq v \leq 4 \} \), the transformation \( T \) is specified by: \[ T: \begin{cases} x = \frac{u}{v}, \\ y = v. \end{cases} \]2. For \( S = \{ (u,v) : 0 \leq u \leq 1, 0 \leq v \leq 1 \} \), the transformation \( T \) is specified by: \[ T: \begin{cases} x = u^2 - v^2, \\ y = 2uv. \end{cases} \]3. For \( S = \{ (u,v) : 0 \leq u \leq 1, 0 \leq v \leq 1 \} \), the transformation \( T \) is specified by: \[ T: \begin{cases} x = u \cos (\pi v), \\ y = u \sin (\pi v). \end{cases} \]**Tasks:**1. Determine the regions \( S \) and \( R \) on the xy-plane using the given transformations.2. Sketch both regions \( S \) and \( R \) for each scenario provided.**Details of Transformations:**1. **First Transformation:** - **Region \( S \)**: \[ \{ (u,v) : 1 \leq u \leq 3, 2 \leq v \leq 4 \} \] - **Transformation \( T \)**: \[ x = \frac{u}{v}, \quad y = v \]2. **Second Transformation:** - **Region \( S \)**: \[ \{ (u,v) : 0 \leq u \leq 1, 0 \leq v \leq 1 \}

Name: Solve for #1 ### Problem 3**Objective:** Find the image R in the xy-pl
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: Solve for #1 ### Problem 3**Objective:** Find the image R in the xy-plane of the region S using the given transformation T. Sketch both R and S.**Given Data:**1. For \( S = \{ (u,v) : 1 \leq u \leq 3, 2 \leq v \leq 4 \} \), the transformation \( T \)