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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

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BuyFindarrow_forward

Calculus: Early Transcendentals

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 = 2x – 1, y = 2x + 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 y=2x1 , y=2x+1 , y=1x and y=3x .

Calculation:

Rewrite the given equations as below,

y2x=1

y2x=1

y+x=1

y+x=3

Let,

u=y2x (1)

v=y+x (2)

By substitute u and v in the above equations to get u=1,u=1 and v=1,v=3 .

Therefore the region of uv plane is S={(u,v)|1u1,1v3}

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Chapter 15 Solutions

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