MATH 120
RECITATION QUESTIONS
(WEEK 8)
1. Find an equation of the tangent plane to the given surface at the specified point.
a
)
z
=
p
4

x
2

2
y
2
,
(1
,

1
,
1)
b
)
z
=
e
x
2

y
2
,
(1
,

1
,
1)
2. Explain why the function
f
(
x, y
) =
x
y
is differentiable at the given point (6
,
3). Then find
the linerization
L
(
x, y
) of the function at that point.
3. Find the linear approximation of the function
f
(
x, y
) =
p
20

x
2

7
y
2
at (2
,
1) and use it
to approximate
f
(1
.
95
,
1
.
08) .
4. Find the differential of the function
u
=
r
s
+ 2
t
.
5. if
z
=
x
2

xy
+ 3
y
2
and (
x, y
) changes from (3
,

1) to (2
.
96
,

0
.
95) , compare the values of
Δ
z
and
dz
.
6. The pressure , volume , and temperature of a mole of an ideal gas are related by the equation
PV
= 8
.
31
T
, where
P
is measured in kilopascals ,
V
in liters, and
T
is kelvins.Use differentials
to find the approximate change in the pressure if the volume increases from 12
L
to 12
.
3
L
and
the temprature decreases from 310
K
to 305
K
.
7.
a
) The function
f
(
x, y
) =
xy
x
2
+
y
2
if (
x, y
)
6
= (0
,
0)
0
if (
x, y
) = (0
,
0)
was graphed in Figure 4 in Stewart.Show that
f
x
(0
,
0) and
f
y
(0
,
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.
 Spring '10
 Tor
 Math, Chain Rule, Derivative, xy x2 +y, Stewart. b

Click to edit the document details