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Math E-21a – Fall 2009 – HW #5 problems
Problems to turn in on Thurs, Oct 8
:
Section 11.2
:
In problems 10 and 11, find the limit, if it exists, or show that the limit does not exist.
10.
3
44
(,) (
0
,
0
)
6
lim
2
xy
x y
x
y
11.
22
0
,
0
)
lim
xy
x
y
Section 11.3
:
37. Find the indicated partial derivative:
(, ,)
;
(
3
,2
,
1
)
z
x
fxyz
f
yz
68. Show that the Cobb-Douglas production function
( ,
)
PLK
bLK
satisfies the equation
()
PP
LK
P
Section 11.4
:
4. Find an equation of the tangent plane to the given surface at the specified point:
ln ,
(1,4,0)
zyx
28. Use differentials to estimate the amount of metal in a closed cylindrical can that is 10 cm high and 4 cm in
diameter if the metal in the top and bottom is 0.1 cm thick and the metal in the sides is 0.05 cm thick.
31. If
R
is the total resistance of three resistors, connected in parallel, with resistances
R
1
,
R
2
, and
R
3
, then
123
1111
R
RRR
If the resistances are measured in ohms as
R
1
= 25
,
R
2
= 40
, and
R
3
= 50
, with a possible error of 0.5%
in each case, estimate the maximum error in the calculated value of
R
.
38. Suppose you need to know an equation of the tangent plane to a surface
S
at the point
P
(2,1,3). You don’t
have an equation for
S
but you know that the curves
1
2 3,1
,3 4
tt
t
t
t
r
and
23
2
() 1
1
,2 1
uu
u
u

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