AP Calculus AB Exam Question

Let f(x) be a function defined by f(x) = 3x^2 - 2x + 1. Determine the value of the following limit:

lim (x -> 2) f(x)

Answer with Step-by-Step Explanation

To find the value of the limit lim (x -> 2) f(x), we substitute x = 2 into the function f(x):

f(2) = 3(2)^2 - 2(2) + 1 = 3(4) - 4 + 1 = 12 - 4 + 1 = 9

Therefore, the value of the limit lim (x -> 2) f(x) is equal to 9.

Explanation:

The limit lim (x -> 2) f(x) represents the value that f(x) approaches as x gets arbitrarily close to 2. To find this value, we substitute x = 2 into the function f(x) and evaluate the resulting expression.

In this case, we substitute x = 2 into f(x) = 3x^2 - 2x + 1:

f(2) = 3(2)^2 - 2(2) + 1.

Simplifying the expression inside the parentheses, we get:

f(2) = 3(4) - 4 + 1.

Evaluating the resulting expression, we have:

f(2) = 12 - 4 + 1.

Finally, combining like terms, we obtain:

f(2) = 9.

Therefore, the value of the limit lim (x -> 2) f(x) is 9.