Show that the vector field11-(-² 22³ sinh(2y - 1) - 32² cosh (2y 1) - 5² In 5-5° In 5)9xy²is conservative by finding all its potential functions.F(x, y, z) =

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Answered: Show that the vector field =(-2 x²y…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Consider the following problem from Science: A mitochondria with velocity vector r' (t) starts out at (-4, 0, 5) at t = 0 and mitochondrias around for 5 seconds. Where is the mitochondria located at time t = 5 if Ir' (t)| dt = 0? A) (-4, 0, 5) B) (-4, 0,5) C) (3, 0, 7) 6. D) Not enough information
Verify Green 's theorem for the vector field F (x, y) = (x^2y, -xy^2) in the triangle OAB defined by the points O (0,0), A (1,0) and B (0.1).
4B
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1) F=Cy+2xz)i+ (x+ z²+1)j +(2yz+x)K Give the Vector field. Protected, ☆Fis the vector fied protected! Your show. If find a Potential function for the vector field "F".
Show all the steps please, thank you
What is the gradient field associated with the potential function f(x,y,z) = 3x2+8y2z3
Find a scalar field, 0, whose gradient is the irrotational vector V = (x² - yz, y² — xz, ² - xy) In other words, find such that Vo=V₁ Note: • Remember that your tutorial has Hints in it, at the end of each chapter. If you're stuck, they are often quite useful! • If the answer is a scalar, you can just type it in the box (using the Calcpad if you like, or using / for fractions, ^ for exponents, shift and - for subscripts, etc.) For multiplication, you can either leave a space, or use *. So x* x = xx = x². Note that this is not the same as x without a space; that will get read as an entirely different variable! • If you need to enter a vector, enter an ordered list of components, so for A you can enter either A = (Az. Ay, A₂) = {Az, Ay, A₂}. Note that the system isn't great with multiplying through by overall factors, so it's better not to write e.g. o= (2A, 2A, 2A₂). + X .. 15 calc Opera Functi Symb Relati
3. Show that the vector field F = -C with C> 0, is conservative and find its potential.
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Show that the vector field =(-2 x²y xy²¹ is conservative by finding all its potential functions. F(x, y, z) = " 2z³ sinh (2y - 1) 3z² cosh (2y - 1) - 5* In 5