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| PAGE: 487 | SET: Exercises | PROBLEM: 53 |
The functions are 
and 
on interval 
.
(a) Label the functions.
Graph the functions 
and 
.
(b)
Observe the graph:
The functions in order of increasing arc length are 
and 
.
(c) Find the arc lengths of the 
and 
.
The functions are and on interval 
.
Definition of the arc length:
If the curve 
, 
, then the length of the curve is defined as, 
.
Find the derivatives of the functions.
, 
, 
and 
.
Find the arc length of 
.
Substitute 
and 
in .
.
Find the arc length of 
.
.
Calculate the arc lengths of 
and .
.
.
(a) Graph of the functions and :
(b) The functions in order of increasing arc length are and .
(c) 
, 
, 
and 
.
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