Final answer:
To find the nonlinear asymptote of the given function, perform long division of the numerator by the denominator. The quotient, without the remainder, will represent the oblique (or slant) asymptote, typically a polynomial of degree one less than the numerator.
Step-by-step explanation:
To find the nonlinear asymptote of the function f(x) = (x5 + 4x3 + 9x2)/(x2 + 4), we can use long division or synthetic division to divide the numerator by the denominator. Since the degree of the numerator is higher than that of the denominator, this function will have an oblique (or slant) asymptote, which is the quotient of this division without the remainder.
We can ignore the remainder because as x approaches infinity, the remainder becomes insignificant compared to the terms with x. In this case, we would expect the leading term of the quotient, after performing the division, to be x3 because that is the result of dividing x5 by x2 and the nonlinear asymptote would be expressed by a cubic function in the form of ax3 + bx2 + cx + d.