(a) Explanation Given: The provided substitutions are u = 3 y − x and v = y − x . Calculation: Consider the region R with points ( 1 , 1 ) , ( 3 , 3 ) , ( 6 , 4 ) and ( 4 , 2 ) . The provided substitutionsare u = 3 y − x and v = y − x . Now, At the point ( 1 , 1 ) , the value of u is; u ( 1 , 1 ) = 3 ( 1 ) − 1 = 2 And, the value of v is; v ( 1 , 1 ) = 1 − 1 = 0 So, the point ( 1 , 1 ) in x y − plane is mapped to the point ( 2 , 0 ) in u v − plane . At the point ( 3 , 3 ) , the value of u is; u ( 3 , 3 ) = 3 ( 3 ) − 3 = 9 − 3 = 6 And, the value of v is; v ( 3 , 3 ) = 3 − 3 = 0 So, the point ( 3 , 3 ) in x y − plane is mapped to the point ( 6 , 0 ) in u v − plane . At the point ( 6 , 4 ) , the value of u is; u ( 6 , 4 ) = 3 ( 4 ) − 6 = 6 And, the value of v is; v ( 6 , 4 ) = 4 − 6 = − 2 So, the point ( 6 , 4 ) in x y − plane is mapped to the point ( 6 , − 2 ) in u v − plane (b) To determine To Calculate: The substitution u = y − x and v = 3 y − x for the transformation from the region R to S and the provided figures are: .

Calculus: Early Transcendental Functions (MindTap Course List)

6th Edition

ISBN: 9781285774770

Author: Ron Larson, Bruce H. Edwards

Publisher: Cengage Learning

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Chapter 14.8, Problem 30E

(a)

To determine

To Calculate: The substitution u=3y−x and v=y−x for the transformation from the region R to S and the provided figures are:

.

(b)

To determine

To Calculate: The substitution u=y−x and v=3y−x for the transformation from the region R to S and the provided figures are:

.

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Chapter 14.8, Problem 29E

Chapter 14.8, Problem 31E

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3 Parallelogram ABCD undergoes a transformation, producing parallelogram A'B'C'D', as shown below. What is the rule for the transformation? # 3 O A. (x, y) + (−y + 7, x) B. (x, y) → (−x + 7, y) C. (x, y) → (-y. +7) D. (x, y) (y 7,2) C 4 $ 95 D A 8 B y 9 2 N U -28 N 4 C Reset Next Ex U acer 口 Sign out

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Chapter 14 Solutions

Calculus: Early Transcendental Functions (MindTap Course List)

Ch. 14.1 - Evaluate the iterated integral: 0433cosrdrd Ch. 14.1 - Prob. 1E Ch. 14.1 - Evaluate the integral: xx2yxdy Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E Ch. 14.1 - Evaluate the integral: 04x2x2ydy Ch. 14.1 - Evaluate the integral: x3x(x2+3y2)dy Ch. 14.1 - Evaluate the integral: eyyylnxxdx;y0 Ch. 14.1 - Evaluate the integral: 1y21y2(x2+y2)dx Ch. 14.1 - Evaluate the integral: 0x2yeyxdy

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The substitution u = 3 y − x and v = y − x for the transformation from the region R to S and the provided figures are: .

Solution Summary: The author calculates the substitutions u=3y-x, and v=y, respectively, for the transformation from the region R to S.

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To Calculate: The substitution u=3y−x and v=y−x for the transformation from the region R to S and the provided figures are:

.

To Calculate: The substitution u=y−x and v=3y−x for the transformation from the region R to S and the provided figures are:

.

Want to see the full answer?

Chapter 14 Solutions

The substitution u = 3 y − x and v = y − x for the transformation from the region R to S and the provided figures are: .

Solution Summary: The author calculates the substitutions u=3y-x, and v=y, respectively, for the transformation from the region R to S.

Videos

To Calculate: The substitution u=3y−x and v=y−x for the transformation from the region R to S and the provided figures are: .

To Calculate: The substitution u=y−x and v=3y−x for the transformation from the region R to S and the provided figures are: .

Want to see the full answer?

Chapter 14 Solutions

To Calculate: The substitution u=3y−x and v=y−x for the transformation from the region R to S and the provided figures are:

.

To Calculate: The substitution u=y−x and v=3y−x for the transformation from the region R to S and the provided figures are:

.