# P29 - the cable to the exterior is R , then the velocity of...

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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.

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