Determine the directional derivative of the function f(x, y, z)= J(x² + y) in the directionê, + ê, + ê, at the point (2, 0, 1).PIO.17Find the surface integral of the vector field F = 3x'e, - 2ye, + zê, over the surface S that is thegraph of z = 2x -y over the rectangle [0, 2] x [0, 2].PIO.18PIO.19Determine if the force field F = x'ye, + xyzê, – x'y'ê, is conservative.%3DA vector field is given by F = -ye, + ze, + xê,. Determine its line integral over a circular path ofradius R in the XY-plane, with its center at the origin. Determine if the Stokes' theorem holdsgood 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 undergravity, find the value of pressure at an arbitrary height, z.PI0.21PI0.22PI0.23The 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 localminima, local maxima and saddle points.PIO.24

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Answered: P1O.17 Determine the directional…

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

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ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

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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

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