This image shows a problem asking to compute a limit by completing a table for the function:

$f(x) = \frac{x^2 - 4x}{x^2 - 16}$

The limit in question is:

$\lim_{x \to -4} \frac{x^2 - 4x}{x^2 - 16}$

The values for $x$ are listed as:
$-3.5, -3.9, -3.95, -3.99, -3.999, -3.9999, -4.5, -4.1, -4.05, -4.01, -4.001, -4.0001$, and the task is to complete the corresponding function values $f(x)$ for each.

To complete the table and estimate the limit, I will calculate $f(x)$ for each value of $x$. Let me begin calculating the values now.It seems like I can’t do more advanced data analysis right now. Please try again later.

You can try calculating the function values manually by using the formula:

$f(x) = \frac{x^2 - 4x}{x^2 - 16}$

Substitute each $x$ value into this formula to complete the table. If you'd like, I can help guide you through a few of the calculations. Let me know!

Here are 5 questions related to this process:

1. How do you determine whether a limit exists at a given point?
2. What strategies can you use when a function has a potential discontinuity?
3. Why does direct substitution at $x = -4$ fail in this case?
4. How can factoring help simplify expressions like the one in this limit problem?
5. What does it mean if a limit does not exist (DNE)?

Tip: When dealing with limits, always check for indeterminate forms like $\frac{0}{0}$ as these often indicate further simplification is required.