To determine the limit of $\lim_{{x \to \infty}} f(x)$, you need to analyze the behavior of the function $f(x)$ as $x$ approaches infinity. However, I don't have the specific function $f(x)$ or the table with $x$-values you mentioned. Here's how you can approach this:

1. Enter $x$-values: Choose a set of large $x$-values, like $x = 10, 100, 1000$, and evaluate $f(x)$ for each.

2. Analyze the function: By observing how $f(x)$ behaves as $x$ increases, you can infer the behavior as $x \to \infty$.

If you provide the function $f(x)$ or the table of values, I can help calculate the limit.

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Here are some related questions to explore:

1. What is the definition of a limit at infinity?
2. How do polynomial functions behave as $x \to \infty$?
3. How do exponential functions behave at large $x$?
4. How does the horizontal asymptote relate to limits?
5. Can a limit approach infinity without reaching a specific value?

Tip: When computing limits, observe if the function stabilizes (i.e., reaches a constant value) or keeps increasing/decreasing.