it is a multivariable calculus problem. Let F(x, y, 2) = (xz, yz, z²).(a) Let S be the cylinder x? + y? = 4, 1 < z < 3, oriented by the outward normal. FindST; F. ds.(b) Suppose that you "close up" the cylinder S in part (a) by adding the disks x? + y² < 4,z = 3, and x2 + y? < 4, z = 1, at the top and bottom, respectively, where the disk atthe top is oriented by the upward normal and the one at the bottom is oriented by thedownward normal. Let S1 be the resulting surface: cylinder, top, and bottom. FindSls, F · dS.

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Answered: Let F(x, y, z) = (xz, yz, z²). (a) Let…

Let F(x, y, z) = (xz, yz, z²). (a) Let S be the cylinder a2 + y² = 4, 1 < z < 3, oriented by the outward normal. Find SS;F · dS.

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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Question

it is a multivariable calculus problem.

Let F(x, y, 2) = (xz, yz, z²).
(a) Let S be the cylinder x? + y? = 4, 1 < z < 3, oriented by the outward normal. Find
ST; F. ds.
(b) Suppose that you "close up" the cylinder S in part (a) by adding the disks x? + y² < 4,
z = 3, and x2 + y? < 4, z = 1, at the top and bottom, respectively, where the disk at
the top is oriented by the upward normal and the one at the bottom is oriented by the
downward normal. Let S1 be the resulting surface: cylinder, top, and bottom. Find
Sls, F · dS.

Study of calculus in one variable to multiple variables. The typical operations involved in multivariate calculus are limits and continuity, partial differentiation, and multiple integration. Major applications are in regression analysis, in finance by quantitative analysis, in engineering and social science to study and build high dimensional systems and exhibit deterministic nature.

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