1
Math E21a – 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
4
4
( ,
)
(0,0)
6
lim
2
x y
x y
x
y
11.
2
2
( ,
)
(0,0)
lim
x y
xy
x
y
Section 11.3
:
37. Find the indicated partial derivative:
( ,
, )
;
(3,2,1)
z
x
f x y z
f
y
z
68. Show that the CobbDouglas production function
( ,
)
P L K
bL K
satisfies the equation
(
)
P
P
L
K
P
L
K
Section 11.4
:
4. Find an equation of the tangent plane to the given surface at the specified point:
ln
,
(1,4,0)
z
y
x
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
1
2
3
1
1
1
1
R
R
R
R
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
2
2
1
( )
2
3 ,1
,3
4
t
t
t
t
t
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '09
 
 Math, Derivative, 0.5%, 0.1 cm, 0.1cm

Click to edit the document details