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Project 29
MAC 2233
1. Examine the function
h
(
x
) =
3 ln(
x
)
x
. What are its domain and intercepts ?
Calculate
h
0
(
x
)
, and
h
00
(
x
)
. Use a number line to determine the interval(s) on which the
function is increasing/decreasing, concave up/down. Are there any local extrema? inﬂection
points?
Now sketch the function
h
(
x
)
below on the axes labeled
A
. Include intercepts, local extrema,
inﬂection points, and asymptotes. Note that
lim
x
→∞
h
(
x
) = 0
A
B
2. If a metal cable of radius
r
is covered by insulation, so that the distance from the center of
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Unformatted text preview: the cable to the exterior is R , then the velocity of an electrical impulse through the cable is: ν =10 x ln( x ) where x is the ratio of r to R (i.e., x = r R ). Find the absolute maximum/minimum value of the function ν ( x ) on the interval ( 0 , 1 ] . Use your work to try to sketch the function on the axes above labeled B . (Note: lim x → + ν ( x ) = 0 )...
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This note was uploaded on 12/27/2011 for the course MAC 2233 taught by Professor Smith during the Spring '08 term at University of Florida.
 Spring '08
 Smith
 Calculus

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