Answered: • • Let > be a potential for the vector… | bartleby

Algebra & Trigonometry with Analytic Geometry

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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Let > be a potential for the vector field F = (−2 y³, −6 xy² − 4 z³, −12 yz² + 4 2). Then the value of
sin((-1.63, 2.06, 0.57) – (0,0,0)) is
-
0.336
-0.931
-0.587
0.440
0.902
0.607
-0.609
0.146

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Let be a potential for the vector field F = (−24 x³ z + 6 xyz², 3 x² z² + 15 y¹, −6 x¹ + 6 x²yz – 10 %). Then the value of sin((-1.63, 2.06, 0.57) - (0,0, 0)) is
Let F1 = (x + y) & + (-x+y)ŷ-2z2 and F2 = 2yx+ (2x + 3z) ŷ +3yî. Calculate the curl and divergence of F1 and F2. Which one can be written as the gradient of a scalar field? Find a suitable potential that does the job.
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Let (4xy-3x²z²)₁ + (2x²)Ĵ − 2x³ zk = (i) Find a scalar potential for F. (x, y, z) = - note: Answer should have "+C" in it, where C is some constant (ii) Find the work done in moving from (1,1,0) to (2, −1, 1) by the above force field. W= (iii) Solve the differential equation (4xy - 3x²²)dx + 2x²dy - 2x³zdz = 0 ☐ = K, where K is a constant
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