Volumes Math Worksheet 6.3 With Answers Page 11
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11Calculus Maximus
WS 6.3: Volumes
x
14. (AP 2002-1) (Calculator Permitted) Let f and g be the functions given by
f x
e and
g x
ln
x .
1
(a) Find the area of the region enclosed by the graphs of f and g between
and
.
x
x
1
2
(b) Find the volume of the solid generated when the region enclosed by the graphs of f and g between
1
x
and
x
1
is revolved about the line
y
4
.
2
(c) Let h be the function given by h x
f x
g x . Find the absolute minimum value of h x on
1
the closed interval
x
1
, and find the absolute maximum value of h x on the closed interval
2
1
x
1
. Show the analysis that leads to your answer.
2
Page 11 of 11
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