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Let u = u(x, y), and let (r, 0) be polar coordinates. Then 1 ||Vu|l? = u? +u r2 Use this to compute ||Vu||2 for u(r, 0) = r cos (0). (Express numbers in exact form. Use symbolic notation and fractions where needed. Give your answer in terms of r and 0.) Use the fact that u(x, y) = x- to compute || Vu||², in terms of x and y, directly. (Express numbers in exact form. Use symbolic notation and fractions where needed. Give your answer in terms of r and 0.)

Let u = u(x, y), and let (r, 0) be polar coordinates. Then 1 ||Vu|l? = u? +u r2 Use this to compute ||Vu||2 for u(r, 0) = r cos (0). (Express numbers in exact form. Use symbolic notation and fractions where needed. Give your answer in terms of r and 0.) Use the fact that u(x, y) = x- to compute || Vu||², in terms of x and y, directly. (Express numbers in exact form. Use symbolic notation and fractions where needed. Give your answer in terms of r and 0.)

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
8th Edition
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Charles P. McKeague, Mark D. Turner
Chapter8: Complex Numbers And Polarcoordinates
Section8.5: Polar Coordinates
Problem 86PS
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Let u = u(x, y), and let (r, 0) be polar coordinates. Then 1 || Vu||? = u? + u Use this to compute || Vu||2 for u(r, 0) = r² cos? (0). (Express numbers in exact form. Use symbolic notation and fractions where needed. Give your answer in terms of r and 0.) ||Vu|? Use the fact that u(x, y) = x- to compute || Vu||², in terms of x and y, directly. (Express numbers in exact form. Use symbolic notation and fractions where needed. Give your answer in terms of r and e.) %3D
Transcribed Image Text:Let u = u(x, y), and let (r, 0) be polar coordinates. Then 1 || Vu||? = u? + u Use this to compute || Vu||2 for u(r, 0) = r² cos? (0). (Express numbers in exact form. Use symbolic notation and fractions where needed. Give your answer in terms of r and 0.) ||Vu|? Use the fact that u(x, y) = x- to compute || Vu||², in terms of x and y, directly. (Express numbers in exact form. Use symbolic notation and fractions where needed. Give your answer in terms of r and e.) %3D
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