Rational functions

**Niles** · Jun10-09, 11:47 AM

Hi all.

I have always wondered: If we e.g. look at functions given by

$LaTeX Code: <BR>f(x) = \\frac{\\cos x}{x^2}, \\quad g(x) = \\frac{\\sin x}{x^2}, \\quad h(x) = \\frac{\\exp x}{x^2},<BR>$
then does the degree of the denominator exceed the degree of the nominator by 1 or by 2?

**Count Iblis** · Jun10-09, 11:55 AM

These are not rational functions. The numerator could be assigned a degree of infinity as they are analytic functions that are not polynomials.

**Niles** · Jun10-09, 11:56 AM

Thank you.