Let F(x,y,z) = < z tan-1(y2),
z3 ln(x2 + 1), z >. Find the flux of...
Let F(x,y,z) = < z tan-1(y2),
z3 ln(x2 + 1), z >. Find the flux of F
across S, the top part of the paraboloid x2 +
y2 + z = 2 that lies above the plane z = 1 and is
oriented upward. Note that S is not a closed surface.
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 = 28
that lies above the plane
z = 3
and is oriented upward.
S
F · dS =
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 x2 + y2 + z = 29
that lies above the plane z = 4 and is oriented upward.
The curried version of let f (x,y,z) = (x,(y,z)) is
let f (x,(y,z)) = (x,(y,z))
Just f (because f is already curried)
let f x y z = (x,(y,z))
let f x y z = x (y z)
Let f(x, y) = − cos(x + y2
) and let a be the point a = ( π/2,
0).
(a) Find the direction in which f
increases most quickly at the point
a.
(b) Find the directional derivative
Duf(a) of f at
a in the direction u = (−5/13 , 12/13)
.
(c) Use Taylor’s formula to calculate a quadratic approximation
to f at a.
Let F= (x2 +
y + 2 + z2) i + (exp(
x2 ) + y2)
j + (3 + x) k . Let a
> 0 and let S be part of the spherical
surface x2 + y2 +
z2 = 2az + 15a2
that is above the x-y plane and the disk formed in the
x-y plane by the circular intersection between the sphere
and the plane. Find the flux of F outward across
S.
1. The function f(x, y) = ln(x3 + 2) / (y2
+ 3) (this function is of a fraction format) :
a.
has a stationary point at (1, 0)
b.
has a stationary point at (0, 0)
c.
has a stationary point at (0, 1)
d.
has no stationary points
2. Which of the following functions don’t have unit elasticity
at P = 6?
a.
Demand: Qd = 24 - 2 P
b.
Demand: Qd = 10/P
c.
Demand: log...