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50. Polar coordinates Suppose that we substitute polar coordi- nates x = r cos 0 and y = r sin 0 in a differentiable function w = f(x, y). a. Show that дw f, cos 0 + f, sin 0 дr and 1 dw -fx sin 0 + f, cos 0. b. Solve the equations in part (a) to express fr and f, in terms of ôw/ðr and ðw/d0. c. Show that (G,F + (5, = () + +(). дw 12 a0

50. Polar coordinates Suppose that we substitute polar coordi- nates x = r cos 0 and y = r sin 0 in a differentiable function w = f(x, y). a. Show that дw f, cos 0 + f, sin 0 дr and 1 dw -fx sin 0 + f, cos 0. b. Solve the equations in part (a) to express fr and f, in terms of ôw/ðr and ðw/d0. c. Show that (G,F + (5, = () + +(). дw 12 a0

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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50. Polar coordinates Suppose that we substitute polar coordi- nates x = r cos 0 and y = r sin 0 in a differentiable function w = f(x, y). a. Show that дw f, cos 0 + f, sin 0 дr and 1 dw -fx sin 0 + f, cos 0. b. Solve the equations in part (a) to express fr and f, in terms of ôw/ðr and ðw/d0. c. Show that (G,F + (5, = () + +(). дw 12 a0
Transcribed Image Text:50. Polar coordinates Suppose that we substitute polar coordi- nates x = r cos 0 and y = r sin 0 in a differentiable function w = f(x, y). a. Show that дw f, cos 0 + f, sin 0 дr and 1 dw -fx sin 0 + f, cos 0. b. Solve the equations in part (a) to express fr and f, in terms of ôw/ðr and ðw/d0. c. Show that (G,F + (5, = () + +(). дw 12 a0
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