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 if x > 0 if x = 0 if r < 0 (**) Let -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)), SC₂F and Q(x, y) = r. 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
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 if x > 0 if x = 0 if r < 0 (**) Let -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)), SC₂F and Q(x, y) = r. 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
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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