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Let where (a) F(x, y) = P(x, y)i + Q(x, y)j. P(x, y) = y 0 -y Determine whether if x > 0 if x = 0 if x < 0 F is conservative or not and explain why. and Q(x, y) = r.

Let where (a) F(x, y) = P(x, y)i + Q(x, y)j. P(x, y) = y 0 -y Determine whether if x > 0 if x = 0 if x < 0 F is conservative or not and explain why. and Q(x, y) = r.

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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Need help with part a). Please explain each step and neatly type up. Thank you :)

 

3. Let where (a) (b) Calculate (c) ( (e) Calculate F(x, y) = P(x, y)i + Q(x, y)j. P(x, y) = Y 0 (**) Let if x > 0 if x = 0 if r < 0 -y (*) Determine whether F is conservative or not and explain why. (**) Consider the following curve parametrised by t: C₁: r(t) = (cos(t), sin(t)), Se₂ and Q(x, y) = x. Sai (*) Find the potential functions of the following vector field. F₁(x, y) = yi + xj F. dr (d) (**) Explain why, for any parametrised curve C₂ contained in the right half plane (x > 0), we have F. dr = Sc₂ π 2 <t< 3π 2 F₁ dr F. dr. C₂ : r(t) = (ln(1 + cos(t)), sin(t)), -≤t≤ ㅠ Savez (Hint: By the result of part (c), F₁ is a conservative vector field.)
Transcribed Image Text:3. Let where (a) (b) Calculate (c) ( (e) Calculate F(x, y) = P(x, y)i + Q(x, y)j. P(x, y) = Y 0 (**) Let if x > 0 if x = 0 if r < 0 -y (*) Determine whether F is conservative or not and explain why. (**) Consider the following curve parametrised by t: C₁: r(t) = (cos(t), sin(t)), Se₂ and Q(x, y) = x. Sai (*) Find the potential functions of the following vector field. F₁(x, y) = yi + xj F. dr (d) (**) Explain why, for any parametrised curve C₂ contained in the right half plane (x > 0), we have F. dr = Sc₂ π 2 <t< 3π 2 F₁ dr F. dr. C₂ : r(t) = (ln(1 + cos(t)), sin(t)), -≤t≤ ㅠ Savez (Hint: By the result of part (c), F₁ is a conservative vector field.)
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