Page:Elements of the Differential and Integral Calculus - Granville - Revised.djvu/184

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Illustrative Example 1. Find the radius of curvature at any point of the catenary .

Solution. .
Substituting in (42),
. Ans.
If the equation of the curve is given in parametric form, find the first and second derivatives of y with respect to x from (A) and (B), §97, namely:
(G) , and
(H) ;

and then substitute the results in (42).[1]

Illustrative Example 2. Find the radius of curvature of the cycloid

Solution. , ;
  , ,
Substituting in (G) and (H), and then in (42), we get
.
Ans.
  1. Substituting (G) and (H), and then in (42) gives .