AP Calculus AB Exam Question:

Find the limit as x approaches infinity of the function f(x) = (3x^2 + 2)/x.

Solution:

To find the limit as x approaches infinity, we can rewrite the expression as follows:

f(x) = (3x^2 + 2)/x = (3x^2/x) + (2/x) = 3x + 2/x.

Now, we can examine the behavior of the function as x approaches infinity.

As x gets larger and larger, the term 2/x approaches 0 since x grows much faster than 2. Hence, it becomes negligible in comparison to the term 3x.

Thus, the limit as x approaches infinity of the function f(x) is the same as the limit of 3x as x approaches infinity.

lim[x -> ∞] (3x + 2/x) = lim[x -> ∞] (3x) = ∞.

Therefore, the limit as x approaches infinity of the function f(x) is infinity.