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Math 20
Winter 2000
Prof. Moore
Final Exam
Directions:
You may use a graphing calculator to compute and graph things during the exam,
but you may not use any notes or books, or receive help from any person.
Show all of your
work, explaining as much as possible.
1. a)
(2 points) Fill in the blank (no explanation necessary): If a function is always
,
then the right endpoint approximation is an underestimate.
b)
(2 points) Fill in the blank (no explanation necessary): If a function is always
,
then the midpoint approximation is an underestimate.
c)
(6 points) Use the trapezoidal approximation to estimate
1
0
e
x
2
dx
, splitting the interval into
three equalsized pieces. Show as much work as possible and give your answer as an approximation
to 4 decimal places.
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2.
A region
A
is bounded by
y
=
√
x
and the
x
axis for the values 0
≤
x
≤
4, and is rotated about
the line
x
= 5 to obtain a solid.
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 Winter '02
 Moore
 Math

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