3. Consider the vector field F (y cos(xy), x cos(xy), - sin(z)) and the curve C parametrised by r(t) = (cos(t), sin(t), 3+ sin(t)) between the points (0, -1, 2) and (0, 1, 4). (a) Calculate the length of C (if you come across an integral you cannot compute by hand, use a machine). (b) Calculate the divergence of F. (c) Calculate the curl of F. (d) Find a potential function f such that F = Vf, or explain why it is not possible. (e) Evaluate F. dr.

3. Consider the vector field F (y cos(xy), x cos(xy), - sin(z)) and the curve C parametrised by r(t) = (cos(t), sin(t), 3+ sin(t)) between the points (0, -1, 2) and (0, 1, 4). (a) Calculate the length of C (if you come across an integral you cannot compute by hand, use a machine). (b) Calculate the divergence of F. (c) Calculate the curl of F. (d) Find a potential function f such that F = Vf, or explain why it is not possible. (e) Evaluate F. dr.

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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