y 4. Surface S is the locus of points satisfying the equation (x² + y²)² + z = 1 with z ≥ 0 and vector field A is given in Cartesian coordinates by A=(y-xz,-x - yz, 1 + z²). -X-32 22 ev ate the ers nd ourse -ya-x X TICTIL late V tving LOper 130 ifficu integra (d) For the vector field F = integrat the value of the line-integral valuate −y(1+z²), x(1+z²), x²+ y² = F. dx, C calculate directly (Stoke's theorem) where C is the circle x² + y2 = 1, z = 0 traversed anticlockwise (in a right-hand sense with respect to the positive z-axis). [3]
y 4. Surface S is the locus of points satisfying the equation (x² + y²)² + z = 1 with z ≥ 0 and vector field A is given in Cartesian coordinates by A=(y-xz,-x - yz, 1 + z²). -X-32 22 ev ate the ers nd ourse -ya-x X TICTIL late V tving LOper 130 ifficu integra (d) For the vector field F = integrat the value of the line-integral valuate −y(1+z²), x(1+z²), x²+ y² = F. dx, C calculate directly (Stoke's theorem) where C is the circle x² + y2 = 1, z = 0 traversed anticlockwise (in a right-hand sense with respect to the positive z-axis). [3]
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![y
4. Surface S is the locus of points satisfying the equation (x² + y²)² + z = 1 with z ≥ 0
and vector field A is given in Cartesian coordinates by A=(y-xz,-x - yz, 1 + z²).
-X-32
22
ev
ate
the
ers
nd ourse
-ya-x
X
TICTIL
late
V
tving
LOper
130
ifficu
integra
(d) For the vector field F =
integrat
the value of the line-integral
valuate
−y(1+z²), x(1+z²), x²+ y²
= F.
dx,
C
calculate directly
(Stoke's theorem)
where C is the circle x² + y2 = 1, z = 0 traversed anticlockwise (in a right-hand
sense with respect to the positive z-axis).
[3]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3011c556-643e-4a01-b0e0-55d8cf24eddf%2F7d60dae6-ce9c-4b29-897d-880a5be9a31a%2Faz5s35fr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:y
4. Surface S is the locus of points satisfying the equation (x² + y²)² + z = 1 with z ≥ 0
and vector field A is given in Cartesian coordinates by A=(y-xz,-x - yz, 1 + z²).
-X-32
22
ev
ate
the
ers
nd ourse
-ya-x
X
TICTIL
late
V
tving
LOper
130
ifficu
integra
(d) For the vector field F =
integrat
the value of the line-integral
valuate
−y(1+z²), x(1+z²), x²+ y²
= F.
dx,
C
calculate directly
(Stoke's theorem)
where C is the circle x² + y2 = 1, z = 0 traversed anticlockwise (in a right-hand
sense with respect to the positive z-axis).
[3]
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