   Chapter 15.9, Problem 14E

Chapter
Section
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 = 4x 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 y=1x , y=4x and the lines y=x , y=4x in the quadrant.

Calculation:

Rewrite the given equations as below,

xy=1

xy=4

yx=1

yx=4

Let,

u=xy (1)

v=yx (2)

By substitute u and v in all the above equations to get u=1,u=4 and v=1,v=4 .

Therefore the region of uv plane is S={(u,v)|1u4,1v4}

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