8. Radius of Curvature

By M. Bourne

We can draw a circle through points on part of a curve. The radius of curvature is the radius of the approximating circle.

The formula for the radius of curvature at the point x for the curve y = f(x) is given by:

radius curvature

Example 1

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Find the radius of curvature for the cubic y = 2x3 − x + 3 at the point x = 1.


Answer


Example 2

[This example was supplied by a reader.]

We have a curve which is defined by the data points (1, 1), (2, 3) and (3,8). We do not know the function for this data. How can we find the radius of curvature?


Answer




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