Explanation Given: G ( u , v ) = ( 2 u , u + v ) . Calculation: Given mapping is G ( u , v ) = ( 2 u , u + v ) . Let x = 2 u , y = u + v a. On the u-axis, v = 0 . So, put v = 0 in the equation y = u + v and we get: G ( u , 0 ) = ( 2 u , u + 0 ) = ( 2 u , u ) So, ( x , y ) = ( 2 u , u ) y = u , x = 2 u Now, put the value of u in y = u and we get: y = u ( since x = 2 u ) y = x 2 Thus, the image of u-axis is: y = x 2 On the v-axis, u = 0 . So, put u = 0 in the equation x = 2 u , y = u + v and we get: G ( 0 , v ) = ( 0 , v ) So, ( x , y ) = ( 0 , v ) x = 0 Thus, the image ofv-axis is:y-axis. b. Given the rectangle R = [ 0 , 5 ] × [ 0 , 7 ] . So, the vertices of the given rectangle will be: [ 0 , 5 ] × [ 0 , 7 ] = ( 0 , 0 ) , ( 5 , 0 ) , ( 0 , 7 ) , ( 5 , 7 ) Now, the images of these vertices are: G ( u , v ) = ( 2 u , u + v ) G ( 0 , 0 ) = ( 2 × 0 , 0 + 0 ) = ( 0 , 0 )

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Question

Chapter 16.6, Problem 1E

To determine

To calculate:

The image under $G (u, v) = (2 u, u + v)$ of the following sets:

a. The u- and v-axes

b. The rectangle $R = [0, 5] \times [0, 7]$

c. The line segment joining $(1, 2) and (5, 3)$

d. The triangle with vertices $(0, 1), (1, 0) and (1, 1)$

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Chapter 16.6, Problem 4PQ

Chapter 16.6, Problem 2E

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Chapter 16 Solutions

Calculus - Standalone book

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The image under G ( u , v ) = ( 2 u , u + v ) of the following sets: a. The u- and v-axes b. The rectangle R = [ 0 , 5 ] × [ 0 , 7 ] c. The line segment joining ( 1 , 2 ) and ( 5 , 3 ) d. The triangle with vertices ( 0 , 1 ) , ( 1 , 0 ) and ( 1 , 1 )

Solution Summary: The author explains how to calculate the image of the u- and v-axes.

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To calculate:

The image under $G (u, v) = (2 u, u + v)$ of the following sets:

a. The u- and v-axes

b. The rectangle $R = [0, 5] \times [0, 7]$

c. The line segment joining $(1, 2) and (5, 3)$

d. The triangle with vertices $(0, 1), (1, 0) and (1, 1)$

Want to see the full answer?

Chapter 16 Solutions

The image under G ( u , v ) = ( 2 u , u + v ) of the following sets: a. The u- and v-axes b. The rectangle R = [ 0 , 5 ] × [ 0 , 7 ] c. The line segment joining ( 1 , 2 ) and ( 5 , 3 ) d. The triangle with vertices ( 0 , 1 ) , ( 1 , 0 ) and ( 1 , 1 )

Solution Summary: The author explains how to calculate the image of the u- and v-axes.

Videos

To calculate: The image under G(u,v)=(2u,u+v)of the following sets: a. The u- and v-axes b. The rectangle R=[0,5]×[0,7] c. The line segment joining (1,2) and (5,3) d. The triangle with vertices (0,1),(1,0) and (1,1)

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Chapter 16 Solutions

To calculate:

The image under $G (u, v) = (2 u, u + v)$ of the following sets:

a. The u- and v-axes

b. The rectangle $R = [0, 5] \times [0, 7]$

c. The line segment joining $(1, 2) and (5, 3)$

d. The triangle with vertices $(0, 1), (1, 0) and (1, 1)$