Let F(x, y, 2) = ryi+ yzj+ zak and C be the boundary of the part of the paraboloid z = 1- z² – y² in the first octant. The curve C is oriented anticlockwise when viewed from above. (a) Which of the following theorems most helpful in evaluating fe F - dr? (1) The Fundamental Theorem of Line Integral (2) Green's Theorem (3) Stokes' Theorem (4) Divergence Theorem (b) Let S:r(u, v) = ui + vj+ (1 – u² – v²)k with u² + v² < 1, u > 0, v > 0 Consider a normal vector (a, b, 1) of S at (, }, ). What is the value a+b? (c) Let vii+vzj+v3k be the curl of F at point (,,5). What is vi +v2 –2v3? (d) Evaluate 20 ſ, F · dr.
Let F(x, y, 2) = ryi+ yzj+ zak and C be the boundary of the part of the paraboloid z = 1- z² – y² in the first octant. The curve C is oriented anticlockwise when viewed from above. (a) Which of the following theorems most helpful in evaluating fe F - dr? (1) The Fundamental Theorem of Line Integral (2) Green's Theorem (3) Stokes' Theorem (4) Divergence Theorem (b) Let S:r(u, v) = ui + vj+ (1 – u² – v²)k with u² + v² < 1, u > 0, v > 0 Consider a normal vector (a, b, 1) of S at (, }, ). What is the value a+b? (c) Let vii+vzj+v3k be the curl of F at point (,,5). What is vi +v2 –2v3? (d) Evaluate 20 ſ, F · dr.
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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Transcribed Image Text:Let
F(x, y, z) = ryi + yzj+ zæk
and C be the boundary of the part of the paraboloid z = 1- x² – y? in the first
octant. The curve C is oriented anticlockwise when viewed from above.
(a) Which of the following theorems most helpful in evaluating ſe F - dr?
(1) The Fundamental Theorem of Line Integral
(2) Green's Theorem
(3) Stokes' Theorem
(4) Divergence Theorem
(b) Let
S:r(u, v) = ui + vj + (1 – u² – v²)k with u² + v² < 1, u > 0, v > 0
Consider a normal vector (a, b, 1) of S at (,, }). What is the value a+b?
(c) Let vii+vzj+v3k be the curl of F at point (,,5). What is vi +v2 –2v3?
23 of 24
(d) Evaluate 20 S. F · dr.
Your answer to (a),
Your answer to (b) ,
Your answer to (c),
Your answer to (d) .
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