AP Calculus AB Exam Question - Limits at Infinity

Question:

Evaluate the following limit:

Answer:

To evaluate the given limit, we can apply the concept of limits at infinity. We will compare the degrees of the numerator and denominator polynomials to determine the behavior of the function as $x$ approaches infinity.

First, let's write the given function in the form of a rational expression:

Now, let's take a look at the degrees of the numerator and denominator polynomials. The highest power of $x$ in the numerator is $x^2$, while the highest power of $x$ in the denominator is $x^3$. Since the degree of the denominator is greater than the degree of the numerator, we can conclude that as $x$ approaches infinity, the fraction will tend to zero.

Hence, the answer to the given limit is: