Problem 24 - College Algebra and Calculus: An Applied Approach

Question

Find the limit. $$ \lim _{x \rightarrow-2} x^{3} $$

Step-by-Step Solution

Answer

The limit as \(x\) approaches \(-2\) of the function \(x^{3}\) is \(-8\).

Step 1: Identify the Function

The function given in the exercise is \(f(x) = x^{3}\). This function is continuous for all real numbers, which means the limit as \(x\) approaches any number exists and is simply \(f\) of that number.

Step 2: Substitute the Limit Point

Substitute \(x = -2\) into the given function. Calculate \(f(-2)\), which is the value of the function at the point \(-2\). This is done as follows: \(f(-2) = (-2)^{3} = -8\).

Step 3: Evaluate the Limit

Since we have calculated the value of the function at \(-2\) and the function is continuous at this point, the limit as \(x\) approaches \(-2\) of the function \(x^{3}\) is simply \(f(-2)\).