Chapter 15.9, Problem 14E

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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.

**14.** *R* is bounded by the hyperbolas *y* = 1/*x, y =* 4/*x* and the lines *y* = *x, y =* 4*x* in the first quadrant

To determine

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

Explanation

**Given:**

A region *R* is bounded by hyperbolas

**Calculation:**

Rewrite the given equations as below,

Let,

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

Therefore the region of *uv* plane is

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