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(a) Sketch the graph of F(0) for 0 ≤0 ≤ 2m. F(0) 2 W r = F(0)=1-sin (0) 1 i. Explain and clearly indicate the points where F(0) = 0. ii. Explain and clearly indicate the points where F attains a local maximum or minimum. (b) By using the results obtained in Part (a) sketch C on the Cartesian zry-plane, using polar coordinates for 0 ≤ 0 ≤ 2m. (c) Write C in parametric form by using: 11/2 3π/2 3w/2 1 2 2m x=r cos (0) = F(0) cos (0) y=rsin (0) F(0) sin (0) ■ 3 0

(a) Sketch the graph of F(0) for 0 ≤0 ≤ 2m. F(0) 2 W r = F(0)=1-sin (0) 1 i. Explain and clearly indicate the points where F(0) = 0. ii. Explain and clearly indicate the points where F attains a local maximum or minimum. (b) By using the results obtained in Part (a) sketch C on the Cartesian zry-plane, using polar coordinates for 0 ≤ 0 ≤ 2m. (c) Write C in parametric form by using: 11/2 3π/2 3w/2 1 2 2m x=r cos (0) = F(0) cos (0) y=rsin (0) F(0) sin (0) ■ 3 0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the curve C defined by (a) Sketch the graph of F(0) for 0 ≤0 ≤ 2π. F(0) 2 1 r = F(0) = 1-sin (0) T/2 (d) Using the parametric form, (c) Write C in parametric form by using: ㅠ i. Explain and clearly indicate the points where F(0) = 0. ii. Explain and clearly indicate the points where F attains a local maximum or minimum. (b) By using the results obtained in Part (a) sketch C on the Cartesian ry-plane, using polar coordinates for 0 ≤ 0 ≤ 2m. π/2 0 3m/2 3π/2 i. Find all horizontal points of tangency. ii. Find all vertical points of tangency. iii. Sketch these points in polar coordinates. 1 2 x = r cos (0) = F(0) cos (0) y=rsin (0) = F(0) sin (0) 2 3 0
Transcribed Image Text:Consider the curve C defined by (a) Sketch the graph of F(0) for 0 ≤0 ≤ 2π. F(0) 2 1 r = F(0) = 1-sin (0) T/2 (d) Using the parametric form, (c) Write C in parametric form by using: ㅠ i. Explain and clearly indicate the points where F(0) = 0. ii. Explain and clearly indicate the points where F attains a local maximum or minimum. (b) By using the results obtained in Part (a) sketch C on the Cartesian ry-plane, using polar coordinates for 0 ≤ 0 ≤ 2m. π/2 0 3m/2 3π/2 i. Find all horizontal points of tangency. ii. Find all vertical points of tangency. iii. Sketch these points in polar coordinates. 1 2 x = r cos (0) = F(0) cos (0) y=rsin (0) = F(0) sin (0) 2 3 0
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