P1O.17 Determine the directional derivative of the function f(x,y, z)= J(x² + y*) in the direction ê, + ê, + ê, at the point (2, 0, I).
P1O.17 Determine the directional derivative of the function f(x,y, z)= J(x² + y*) in the direction ê, + ê, + ê, at the point (2, 0, I).
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
![Determine the directional derivative of the function f(x, y, z)= J(x² + y) in the direction
ê, + ê, + ê, at the point (2, 0, 1).
PIO.17
Find the surface integral of the vector field F = 3x'e, - 2ye, + zê, over the surface S that is the
graph of z = 2x -y over the rectangle [0, 2] x [0, 2].
PIO.18
PIO.19
Determine if the force field F = x'ye, + xyzê, – x'y'ê, is conservative.
%3D
A vector field is given by F = -ye, + ze, + xê,. Determine its line integral over a circular path of
radius R in the XY-plane, with its center at the origin. Determine if the Stokes' theorem holds
good for this circular path, by considering the following surfaces:
PI0.20
(i) the plane of the circle, and (ii) surface of a cylinder of height h erected on the circle.
Determine the curl of the following vectors fields: (a) p cos pê, - p sin pê (b) -ě,.
For the steady irrotational flow of incompressible, non-viscous liquids, if the flow occurs under
gravity, find the value of pressure at an arbitrary height, z.
PI0.21
PI0.22
PI0.23
The density field of a plane, steady state fluid flow given by p(x1, x2)=kx,x2 where k is constant.
Determine the form of the velocity field if the fluid is incompressible.
Determine the stationary points of the function f(x, y) = 3x'y + y -4x - 4y + 6. Find its local
minima, local maxima and saddle points.
PIO.24](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F368d62f4-35b7-41a2-9981-699536396cec%2F974f84fe-e744-4a6f-90d2-a2ca1388b78d%2Flgcso7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Determine the directional derivative of the function f(x, y, z)= J(x² + y) in the direction
ê, + ê, + ê, at the point (2, 0, 1).
PIO.17
Find the surface integral of the vector field F = 3x'e, - 2ye, + zê, over the surface S that is the
graph of z = 2x -y over the rectangle [0, 2] x [0, 2].
PIO.18
PIO.19
Determine if the force field F = x'ye, + xyzê, – x'y'ê, is conservative.
%3D
A vector field is given by F = -ye, + ze, + xê,. Determine its line integral over a circular path of
radius R in the XY-plane, with its center at the origin. Determine if the Stokes' theorem holds
good for this circular path, by considering the following surfaces:
PI0.20
(i) the plane of the circle, and (ii) surface of a cylinder of height h erected on the circle.
Determine the curl of the following vectors fields: (a) p cos pê, - p sin pê (b) -ě,.
For the steady irrotational flow of incompressible, non-viscous liquids, if the flow occurs under
gravity, find the value of pressure at an arbitrary height, z.
PI0.21
PI0.22
PI0.23
The density field of a plane, steady state fluid flow given by p(x1, x2)=kx,x2 where k is constant.
Determine the form of the velocity field if the fluid is incompressible.
Determine the stationary points of the function f(x, y) = 3x'y + y -4x - 4y + 6. Find its local
minima, local maxima and saddle points.
PIO.24
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