Solutions to Quiz 4A
www.math.ufl.edu/˜harringt
February 9, 2008
1. Suppose that
g
(
x
) is a continuous function on [1
,
2]. Furthermore, we
know that
g
(1)
<
0 and
g
(2)
>
0. What does the Intermediate Value
Theorem tell us?
The Intermediate Value tells use that there exists a
c
(may not be
unique) in the interval of (1
,
2) such that
f
(
c
) = 0.
NOTE:
Since
g
(1) = 0 and
g
(2) = 0 then we know
c
∈
(1
,
2). If you
put [1
,
2] that will be acceptable for this quiz.
2. Evaluate the following limit: lim
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 Fall '08
 ALL
 Math, Calculus, Geometry, Topology, Intermediate Value Theorem, lim, Continuous function

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