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Unformatted text preview: h ( x ) below. Label all intercepts, local extrema, inﬂection points, removable discontinuities, and asymptotes. 2. If a metal cable of radius r is covered by insulation so that the distance from the center of the cable to the exterior is R , the velocity of an electrical impulse through the cable is: ν =-cx ln( x ) for some positive constant c , where x is the ratio of r to R (i.e., x = r/R ). Use some of the techniques learned so far to sketch a graph of the function ν ( x ) . (To evaluate lim x → + ν ( x ) , use L’Hˆopital’s Rule; if you have trouble with the c , take c = 1 .) Looking at your graph, what ratio x yields the maximum velocity for the impulse? How can you tell this just from your number line for the derivative ?...
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This note was uploaded on 04/04/2012 for the course MAC 2311 taught by Professor All during the Spring '08 term at University of Florida.
- Spring '08