Problem #10:Find the flux of F(x, y, z) = yi − xj + 8k across S, wherehelicoidSisthewithvectorequationr(u, v) = (u cos v, u sin v, v), 0 ≤ u ≤ 1,0 ≤v ≤ 2.

Answered: Image /qna-images/answer/4af53256-6874-495d-8b4b-f366447d3fcc.jpg

Answered: Problem #10: Find the flux of F(x, y,…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

Find a vector u E K such that, at the point (2,1, –1), the function f(, y, 2) = -y' + 222 + 2² has its greatest rate of increase in the direction of u. Ou= (-4, 2, 1) = (8,-3,-2) = (3,-2,-8) u (8, –3, 2) None of the others
(1) Give an example of a function z = f(x, y) and a unit vector i such that f.(0,0) = 2, fy(0,0) = 1 and fã(0,0) is negative.
2. Find the directional derivative of f(x,y,z) = x²y + yz² at P(1,–1,3) in the direction of vector (1,5, 2). -2 а) V30 3 b) V30 c) V30 7 d) 30 e) None of the above
Please give me answers in 5min I will give you like sure
Suppose f(z) = u(x, y) +iv(x, y) is differentiable at zo = xo+iyo, with f'(zo) # 0. Show that the vectors Vu(xo, yo) and Vv(xo, yo) are perpendicular and have the same magnitude. Express this magnitude in terms of f'(zo).
3. Let i, j, k denote the unit vectors along the three coordinate axes. Let v(t) = ti+ sintj + costk and w(t) = 3ti + 2k. (a) Compute (v.w)' (t) directly and check your answer by using the product rule (for the dot product, stated in the class). Note that the dot above, is the dot product of vectors and denotes the derivative. (b) Compute (v x w)'(t) directly and check your answer by using the product rule (for the cross product, again stated in the class). Note that the x above, is the cross product of vectors.
3. (b) Let f(x, y) = log((ry - 2)²), u =(³, 4). i. Calculate the directional derivative Vaf (3, 1). ii. Determine the unit vector (direction) u for which Vaf (3, 1) is maximal.
Compute the directional derivatives of the following functions along unit vectors at the indicated points in directions parallel to the given vector. (a) f(x, y) = x, (xo, Y) = (e, e), d = 9i + 40j (b) f(x, y, z) = ex + yz, (xo, Yo, Zo) = (1, 1, 1), d = (4, −7, 7) (c) f(x, y, z) = xyz, (xo, Yo, Zo) = (1, 0, 1), d = (1, 0, -1) Screenshot
SOLVE STEP BY STEP IN DIGITAL FORMAT PLEASE Through the point P(-2,-7) tangents are drawn to the ellipse 2x² + y² + 2x-3y - 2 = 0; determine the equations of the tangents and the points of tangency +

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS

Problem #10: Find the flux of F(x, y, z) = yi − xj + 8k across S, where helicoid S is the with vector equation r(u, v) = (u cos v, u sin v, v), 0 ≤ u ≤ 1,0 ≤v ≤ 2.