Example 1. From the family of the graphs of the polynomial functions
We may seek the osculating hyperbola from the three-parametric family
Removing the denominators and differentiating six times successively yield the equations
Into these equations we can substitute the coordinates of the contact point and the values of the derivatives
of cosine in that point; the values are . The first, third and fifth of the equations (2) give the result , whence the osculating hyperbola is
When we substitute the pertinent values of the cosine derivatives into the two last equations (2), we see that only the former of them is satisfied. It means that the order of contact between the cosine curve and the hyperbola is 5.
The order of contact is only 3.
|Date of creation||2013-03-22 17:57:17|
|Last modified on||2013-03-22 17:57:17|
|Last modified by||pahio (2872)|