Question

when z=f(x,y), where tan(xyz)=x+y+z, find az/ax and az/ay

Answer #1

q.1.(a)
The following system of linear equations has an infinite number
of solutions
x+y−25 z=3
x−5 y+165 z=0
4 x−14 y+465 z=3
Solve the system and find the solution in the form
x(vector)=ta(vector)+b(vector)→, where t is a free
parameter.
When you write your solution below, however, only write the part
a(vector=⎡⎣⎢ax ay az⎤⎦⎥ as a unit column vector with the
first coordinate positive. Write the results accurate to
the 3rd decimal place.
ax =
ay =
az =

Given the function f (x, y) = ax^2
2 + 2xy + ay.y
2-ax-ay. Take
for a an integer value that is either greater than 1 or less
than -1, and
then determine the critical point of this function. Then
indicate whether it is
is a local maximum, a local minimum or a saddle point.
Given the function f (x, y) = ax^2 +2 + 2xy + ay^2-2-ax-ay.
Take
for a an integer value that is either greater than 1...

1- find the divergence of F(x,y,z) = <e^x(y),x^2(z),xyz>
at (1,-1,3).
2- find the curl of F(x,y,z)= <xyz,y^2(z),x^2(y)z^3> at
(0,-2,2)

Let F(x, y, z) = z tan−1(y^2)i + z^3 ln(x^2 + 7)j + zk. Find the
flux of F across S, the part of the paraboloid x^2 + y^2 + z = 29
that lies above the plane z = 4 and is oriented upward.

use Lagrange multipliers to find the maximum of F(x,y,z)=xyz
with the constraint H(x,y,z)=x^2+y^2+z^2-8=0

Let F(x, y,
z) = z
tan−1(y2)i
+ z3
ln(x2 + 9)j +
zk. Find the flux of
F across S, the part of the paraboloid
x2 + y2 +
z = 7 that lies above the plane
z = 3 and is oriented upward.

Let F(x, y, z) = z tan−1(y2)i + z3 ln(x2 + 7)j + zk. Find the
flux of F across S, the part of the paraboloid x2 + y2 + z = 6 that
lies above the plane z = 5 and is oriented upward.

Let
F(x, y,
z) = z
tan−1(y2)i
+ z3
ln(x2 + 8)j +
zk.
Find the flux of F across S, the part
of the paraboloid
x2 +
y2 + z = 6
that lies above the plane
z = 5
and is oriented upward.
S
F · dS
=

use stoke's theorem to find ∬ (curl F) * dS where F (x,y,z) =
<y, 2x, x+y+z> and and S is the upper half of the sphere x^2
+ y^2 +z^2 =1, oriented outward

Find the angle between the curves y = cot x and y = tan x where
they intersect between 0 < x < pi/2. Using Vector forms.

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