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17A
Practice Final
Fall 2010
1.
Differentiate: a)
y
=
x
x
2
+
3
e
sin
x
b)
f
(
x
)
=
ln
2
!
x
x
2
"
#
$
%
’
2.
If
f
(
x
)
=
x
!
cos(
x
)
find
d
dx
f
!
1
(
!
1)
3.
The radius of a circle is measured with a relative error of 5%. What will the relative error be if
you use this measurement to calculate the are of the circle?
4.
A cylindrical cell characterized by radius
r
and height
h
is to be enclosed in a membrane that has
a given constant surface area of
12
!
. Find the
r
and
h
that maximize the enclosed cell volume.
5. Consider the reaction
A
+
B
!
K
If y represents the amount (in mols) of A at time t, x represents the amount of B (in mols) at
time t, and z represents the amount of K (in mols) at time t. The reaction rates can be
modeled by:
e
y
2
+
xy
=
z
.
If the amount of A is increasing at 5 mol/min and the amount of B is decreasing at 3
mol/min, how is the amount of K changing when there are 10 mols A and 5 mols of B?
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This note was uploaded on 05/31/2011 for the course MATH 17A taught by Professor Lyles during the Spring '08 term at UC Davis.
 Spring '08
 LYLES

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