Since we want a specific potential function, we will choose K = 0, and so 1x3 3 Dy3. We know that if the curve C is given by r(t) with a sts b, the + F. dr = f(r(b)) – f(r(a)).

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter10: Analytic Geometry
Section10.6: The Three-dimensional Coordinate System
Problem 41E: Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?
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Use part (a) to evaluate
Vf • dr along the given curve C.
Step 1
Since we want a specific potential function, we will choose K = 0, and so
f(x, y) = x
1x3 +
3
3. We know that if the curve C is given by r(t) with a <t s b, then
F• dr = f(r(b)) – f(r(a)).
Transcribed Image Text:Use part (a) to evaluate Vf • dr along the given curve C. Step 1 Since we want a specific potential function, we will choose K = 0, and so f(x, y) = x 1x3 + 3 3. We know that if the curve C is given by r(t) with a <t s b, then F• dr = f(r(b)) – f(r(a)).
Consider F and C below.
F(x, y) = x2 i + y2 j
C is the arc of the parabola y = 3x2 from (-2, 12) to (-1, 3)
Exercise (a)
Find a function f such that F = Vf.
Step 1
If Vf(x, y) = F(x, y) = x²i + y²j, then
fx(x, y) =
and
fy(x, y) =
Transcribed Image Text:Consider F and C below. F(x, y) = x2 i + y2 j C is the arc of the parabola y = 3x2 from (-2, 12) to (-1, 3) Exercise (a) Find a function f such that F = Vf. Step 1 If Vf(x, y) = F(x, y) = x²i + y²j, then fx(x, y) = and fy(x, y) =
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