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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