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Homework 12
Section 3.8 dy 1. (4) Compute dx for y= cosh(x4 )
.
2 2. (4) Find the derivative of dy 3. (4) Find dx for y= f (t) = −t2 sinh2 t − cosh2 t sinh(x2 )
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x . Simplify your answer. 4. (8) The cable between two towers of an overhead utility cable hangs in the shape of
the curve y=
where T wx
T
cosh
,
w
T is the tension in the cable at its lowest point and w is the weight of the cable per unit length. Suppose the cable stretches between the points T
x = −w and x= T
.
w Sketch a graph of the cable. Find an expression for the sag in the cable (the distance
between the highest point on the cable and the lowest point on the cable). Show, by computing both sides, that y= w
T 1 + (y )2 . ...
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 Spring '08
 KENNEDY
 Derivative, Graph of a function, lowest point, compute dx, overhead utility cable

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