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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.
 Fall '07
 BAHLS
 Derivative

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