Stewart6e3_7Density

# Stewart6e3_7Density - MATH 191, Sections 1 and 3 Calculus I...

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MATH 191, Sections 1 and 3 Calculus I Fall 2007 Section 3.7: Another physical application Let’s investigate one more application of calculus to physics, before we move on to talking about the way the derivative of a function tells us much about the function’s behavior. If we are given a uniform piece of wire or some other “linear” shape, we know that its linear density ρ is ; that is, the per unit length is the same throughout the length of the wire. However, it’s possible that the amount of “stuﬀ” contained in any given chunk of the wire varies with the position of the wire. (This might be the case, for instance, if the wire is made of some composite of materials that varies along its length.) Let’s lay our wire along the x -axis, with one end at the origin. We then denote by m ( x ) the mass of the portion of the wire lying to the left of the point x , as shown in the picture you’ll provide below: If we wish to determine the mass of a small “chunk” of the wire, lying between

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## This note was uploaded on 04/08/2008 for the course MATH 191 taught by Professor Bahls during the Fall '07 term at UNC Asheville.

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Stewart6e3_7Density - MATH 191, Sections 1 and 3 Calculus I...

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