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The problem asks to compute the limit:

\[
\lim_{x \to 8} \frac{\sqrt{1 - x} - 3}{8 + x}
\]

Let's solve it step by step:

### Step 1: Substitute \( x = 8 \)

Substituting directly into the limit expression:

\[
\frac{\sqrt{1 - 8} - 3}{8 + 8} = \frac{\sqrt{-7} - 3}{16}
\]

Since \(\sqrt{-7}\) is not a real number, this limit does not exist in the real number system. However, we may need to interpret the problem differently or check if it should be evaluated within a complex domain. If the context is real numbers, this limit is undefined.

Would you like further clarification or a deeper exploration of this limit?

Here are 5 related questions you could explore:

1. What happens if we attempt to evaluate the limit from the left and right side separately?
2. How can we extend the problem to evaluate the limit in the complex plane?
3. What other methods exist to evaluate limits involving square roots?
4. Can limits involving imaginary numbers have real interpretations in certain contexts?
5. How would the limit change if we adjusted the function to avoid imaginary values?

**Tip:** Always check for non-real numbers when evaluating limits with square roots to determine the nature of the solution (real or complex).

Вычислить предел: lim_{x -> 8} (sqrt(1 - x) - 3) / (8 + x)

Learn how to compute the limit of (sqrt(1 - x) - 3) / (8 + x) as x approaches 8. This example involves handling indeterminate forms and square roots, a common topic in Calculus. Step-by-step solutions and insights into real versus complex number limits.

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