what is the oblique asymptote of this rational function: (x ^ 3) / (x ^ 2+1)

To find the oblique asymptote of a rational function, you need to determine the ratio of the highest degree terms in the numerator and denominator.

In this case, the highest degree term in the numerator is x^3, and the highest degree term in the denominator is x^2. To find their ratio, divide the numerator by the denominator:

(x^3) / (x^2+1)

Dividing x^3 by x^2 gives a quotient of x, and dividing x^3 by 1 gives a quotient of x^3. Therefore, the ratio of the highest degree terms is x^3 / x^2, which simplifies to x.

This means that the oblique asymptote of the rational function is a straight line with the equation y = x.