Chapter 15.9, Problem 11E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

A region *R* in the *xy*-plane is given. Find equations for a transformation *T* that maps a rectangular region *S* in the *uv*-plane onto *R*, where the sides of *S* are parallel to the *u-* and *v*-axes.

**11.** *R* is bounded by *y* = 2*x* – 1, *y* = 2*x* + 1, *y* = 1 – *x*, *y* = 3 – *x*

To determine

**To find:** Equation for the transformation *T* maps with given rectangular region *S*.

Explanation

**Given:**

A region *R* is bounded by

**Calculation:**

Rewrite the given equations as below,

Let,

By substitute *u* and *v* in the above equations to get

Therefore the region of *uv* plane is

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