Explanation Given: G ( u , v ) = ( u 2 , v ) . Calculation: Given mapping is G ( u , v ) = ( u 2 , v ) . Let x = u 2 , y = v a. On the u-axis, v = 0 . So, put v = 0 in the equation y = v and we get: G ( u , 0 ) = ( u 2 , 0 ) = ( u 2 ) So, ( x , y ) = ( u 2 , 0 ) y = 0 Thus, the image ofu-axis is:x-axis. On the v-axis, u = 0 . So, put u = 0 in the equation x = u 2 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 = [ − 1 , 1 ] × [ − 1 , 1 ] . So, the vertices of the given rectangle will be: [ − 1 , 1 ] × [ − 1 , 1 ] = ( − 1 , − 1 ) , ( − 1 , 1 ) , ( 1 , − 1 ) , ( 1 , 1 ) Now, the images of these vertices are: G ( u , v ) = ( u 2 , v ) G ( − 1 , − 1 ) = ( ( − 1 ) 2 , − 1 ) = ( 1

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on …

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Chapter 16.6, Problem 3E

To determine

To calculate:

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

a. The u- and v-axes

b. The rectangle $R = [- 1, 1] \times [- 1, 1]$

c. The line segment joining $(0, 0) and (1, 1)$

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

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Chapter 16.6, Problem 2E

Chapter 16.6, Problem 4E

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Chapter 16 Solutions

Calculus - Standalone book

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

a. The u- and v-axes

b. The rectangle $R = [- 1, 1] \times [- 1, 1]$

c. The line segment joining $(0, 0) and (1, 1)$

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

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Chapter 16 Solutions

The image under G ( u , v ) = ( u 2 , v ) of the following sets: a. The u- and v-axes b. The rectangle R = [ − 1 , 1 ] × [ − 1 , 1 ] c. The line segment joining ( 0 , 0 ) and ( 1 , 1 ) d. The triangle with vertices ( 0 , 0 ) , ( 0 , 1 ) 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)=(u2,v)of the following sets: a. The u- and v-axes b. The rectangle R=[−1,1]×[−1,1] c. The line segment joining (0,0) and (1,1) d. The triangle with vertices (0,0),(0,1) and (1,1)

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Chapter 16 Solutions

To calculate:

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

a. The u- and v-axes

b. The rectangle $R = [- 1, 1] \times [- 1, 1]$

c. The line segment joining $(0, 0) and (1, 1)$

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