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5. Let S = (0, 1] × [0, 2.7) and define T(r, 0) = (rcos 0, r sin 0). Determine the image set S Show that T is one-to-one on S. %3D

5. Let S = (0, 1] × [0, 2.7) and define T(r, 0) = (rcos 0, r sin 0). Determine the image set S Show that T is one-to-one on S. %3D

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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(b) T(x, y) (, y) (c) T(x, y) (, D) (d) T(x, y) (sin x, cos y) 2. Determine if the following functions T: R2R2 an are one-to-one and/or onto. (a) T(x, y, z) = (2x+ y+3z, 3y- 4z, 5x) (b) T(x, y, 2) = (y sin x, zcos y, xy) (c) T(x, y, 2) = (xy, yz, xz) (d) T(x, y, 2) = (c", o', e) %3D %3D 3. Let D be a square with vertices (0, 0), (1, 1), (2, 0), (1, -1) and D* be a parallelogram with vertices (0, 0), (1, 2), (2, 1), (1, -1). Find a linear map T taking D* onto D. 10. 4. Let D be a parallelogram with vertices (0,0), (-1, 3), (–2, 0), (–1, –3). Let D- 10 1 v 1O 11 Find a linear man T such that Highlight Underline P Edit Tex VP. Erase ext Transl. 5. Let S = (0, 1] × [0, 2.7) and define T(r, 0) = (rcos 0, rsin ). Determine the image set S Show that T is one-to-one on S 11. L on MacBook Pro
Transcribed Image Text:(b) T(x, y) (, y) (c) T(x, y) (, D) (d) T(x, y) (sin x, cos y) 2. Determine if the following functions T: R2R2 an are one-to-one and/or onto. (a) T(x, y, z) = (2x+ y+3z, 3y- 4z, 5x) (b) T(x, y, 2) = (y sin x, zcos y, xy) (c) T(x, y, 2) = (xy, yz, xz) (d) T(x, y, 2) = (c", o', e) %3D %3D 3. Let D be a square with vertices (0, 0), (1, 1), (2, 0), (1, -1) and D* be a parallelogram with vertices (0, 0), (1, 2), (2, 1), (1, -1). Find a linear map T taking D* onto D. 10. 4. Let D be a parallelogram with vertices (0,0), (-1, 3), (–2, 0), (–1, –3). Let D- 10 1 v 1O 11 Find a linear man T such that Highlight Underline P Edit Tex VP. Erase ext Transl. 5. Let S = (0, 1] × [0, 2.7) and define T(r, 0) = (rcos 0, rsin ). Determine the image set S Show that T is one-to-one on S 11. L on MacBook Pro
erts [WI22] 21 n, yersino missing0-2r OSTEI rectagle but while hop edge & LH edge wれ remaved. ( 3 So We hate everything inside. "Notes.pdf Lecture8Notes.pdf cse11-pa3-starte...zip Aa
Transcribed Image Text:erts [WI22] 21 n, yersino missing0-2r OSTEI rectagle but while hop edge & LH edge wれ remaved. ( 3 So We hate everything inside. "Notes.pdf Lecture8Notes.pdf cse11-pa3-starte...zip Aa
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