Consider the vector field F (x, y, z) = xi + yj + zk. a) Find a function f such that F = Vf and f(0, 0, 0) = 0. f(x, y, z) = b) Use part a) to compute the work done by F on a particle moving along the curve C given by r (t) = (1 + 5 sin t)i + (1 + 3 sin² t)j + (1+3 sin³ t)k, 0/
Consider the vector field F (x, y, z) = xi + yj + zk. a) Find a function f such that F = Vf and f(0, 0, 0) = 0. f(x, y, z) = b) Use part a) to compute the work done by F on a particle moving along the curve C given by r (t) = (1 + 5 sin t)i + (1 + 3 sin² t)j + (1+3 sin³ t)k, 0/
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 78E
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![Consider the vector field F (x, y, z) = xi + yj + zk.
a) Find a function f such that F
=
Vf and
f(0,0,0) = 0.
f(x, y, z) =
b) Use part a) to compute the work done by F on a
particle moving along the curve C given by
r (t) = (1 + 5 sin t)i + (1 + 3 sin² t)j + (1+3 sin³ t)k, 0≤t≤ 10](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff35f8f89-65fc-4b90-98e9-68f8eaa1b3da%2F2a80c6fc-8bd5-4394-b688-986565e6b634%2Fzt1ku0v_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the vector field F (x, y, z) = xi + yj + zk.
a) Find a function f such that F
=
Vf and
f(0,0,0) = 0.
f(x, y, z) =
b) Use part a) to compute the work done by F on a
particle moving along the curve C given by
r (t) = (1 + 5 sin t)i + (1 + 3 sin² t)j + (1+3 sin³ t)k, 0≤t≤ 10
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