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Math 16a Problem List
Spring 2008
H. Woodin
1. For each of the following, determine if the limit exists and compute the
limit if it does exist.
(a) lim
x
→
0
±
x
q
1 + (1
/x
2
)
²
(b) lim
x
→
0
±
x
2
q
1 + (1
/x
4
)
²
2. Find the points on the graph of
y
=
x
3
+ 1001 where the tangent is
parallel to the line
y
= 3
x
.
3. Find the derivative of
y
= (
x
3
+
x
2
+ 2001)
16
at
x
= 1.
4. Find the equation of the line which is tangent to the curve
y
= 4
x
1
/
4
at the point where
x
= 16.
5. Suppose
f
(
x
) =

2
x
+ 1

3
. Find
f
0
(
x
).
1
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View Full Document 6. Suppose
f
(
x
) is a function with domain (0
,
∞
) and that
f
(
x
) =
x
2

4
x
+ 3
x
2

1
for
x
6
= 1 and that
f
(1) =
a
. Suppose
f
(
x
) is continuous at
x
= 1.
Find
a
.
7. Using the derivative, ﬁnd an approximate value of ln 3 in terms of
e
by
using the fact that ln
e
= 1.
8. Suppose
g
(
x
) =
1
3
x
3

x
.
(a) Identify the inﬂection points of
g
(
x
) or explain why there are none.
(b) Find the maximum value of
g
(
x
) for 0
≤
x
≤
2.
(c) Does
g
(
x
) have a mimimum value for
x >
2? Why?
9. Consider the curve deﬁned by the equation
x
3
+
y
2
x
=
y
.
(a) Find
dy/dx
by implicit diﬀerentiation.
(b) Find the point (
a,b
) on the curve where
a >
0 and the line tangent
to the curve is vertical.
10. Find the minimum possible value of 3
a
+ 5
b
given that
a >
0,
b >
0
and that
a
·
b
= 75.
11. Find the minimum value of
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This note was uploaded on 05/20/2008 for the course MATH 16A taught by Professor Stankova during the Spring '07 term at University of California, Berkeley.
 Spring '07
 Stankova
 Math

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