Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN: 9781133382119
Author: Swokowski
Publisher: Cengage
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Need help with part c). Please explain each step and neatly type up. Thank you :)
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.)
Expert Solution
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Step 1
To Find the Potential Function of the Vector field
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