Question

* f*(

* x* +

x^{2} + y^{2} |

; *f*_{x}(5,
−3)

Answer #1

4.4-JG1 Given the following joint density function in Example
4.4-1:
fx,y(x,y)=(2/15)d(x-x1)d(y-y1)+(3/15)d(x-x2)d(y-y1)+(1/15)d(x-x2)d(y-y2)+(4/15)d(x-x1)d(y-y3)
a) Determine fx(x|y=y1) Ans: 0.4d(x-x1)+0.6d(x-x2)
b) Determine fx(x|y=y2) Ans: 1d(x-x2)
c) Determine fy(y|x=x1) Ans: (1/3)d(y-y1)+(2/3)d(y-y3)
d) Determine fx(y|x=x2) Ans:
(3/9)d(y-y1)+(1/9)d(y-y2)+(5/9)d(y-y3)
4.4-JG2
Given fx,y(x,y)=2(1-xy) for 0 a) fx(x|y=0.5) (Point Conditioning)
Ans: (4/3)(1-x/2)
b) fx(x|0.5

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.

Consider the following five utility functions.
G(x,y) = x2 + 3 y2
H(x,y) =ln(x) + ln(2y)
L(x,y) = x1/2 + y1/2
U(x,y) =x y
W(x,y) = (4x+2y)2
Z(x,y) = min(3x ,y)
In the case of which function or functions can the Method of
Lagrange be used to find the complete solution to the consumer's
utility maximization problem?
a.
H
b.
U
c.
G
d.
Z
e.
L
f.
W
g.
None.

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
=

(1 point)
Find all the first and second order partial derivatives of
f(x,y)=7sin(2x+y)−2cos(x−y)
A. ∂f∂x=fx=∂f∂x=fx=
B. ∂f∂y=fy=∂f∂y=fy=
C. ∂2f∂x2=fxx=∂2f∂x2=fxx=
D. ∂2f∂y2=fyy=∂2f∂y2=fyy=
E. ∂2f∂x∂y=fyx=∂2f∂x∂y=fyx=
F. ∂2f∂y∂x=fxy=∂2f∂y∂x=fxy=

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 joint CDF Fx,y (x,y) = сxy(x2 + y2)
for 0 ≤ x ≤ 1, 0 ≤ y ≤ 1.
Find а) constant с.
b) Fx|y (x|y) for x = 0.5, y = 0.5.

. Let f(x, y) = x2 y(2 − x + y2
)5 − 4x2 (1 + x + y)7 +
x3 y2 (1 − 3x − y)8 . Find the
coefficient of x5y3 in the expansion of f(x,
y).

Find the directional derivative of the function
f(x,y,z)=ln(x2+y2−1)+y+6z at the point (1,1,0) in the direction of
the vector v→=i→−2j→+2k→

1)
If z=Ln(x2+y2 ) , x=e-1
,y=et the total derivative dz/dt will
become--------------
Select one:
A. dz/dt=2x/x2+ y2 . (-e-t) -
2x/(x2+ y2 ). et
B. dz/dt=2x/x2+ y2 .
(-e-t)+2x/(x2+ y2 ).
e-t
C. dz/dt=2x/x2+ y2 .
(-e-t)+2x/(x2+ y2 ).
et
D. dz/dt=2x/x2+ y2 .
(e-t)+2x/(x2+ y2 ).
et
2)
The second order partial derivative with respect to x of
f(x,y)=cos(x)+xyexy+xsin(y) is-------------
Select one:
A. ∂/∂x(∂f/∂x) = 2y2exy +
xy3exy
B. ∂/∂x(∂f/∂x) = −cos(x) + 2y2exy +
xy3exy + sin(y)...

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