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Yes, the limit exists, and its value is \( \frac{1}{72} \).

Would you like more details or have any questions? Here are five related questions to expand on this concept:

1. How does simplifying an expression help in computing limits?
2. What is the difference between evaluating a limit and directly substituting the value?
3. What happens when a limit results in an indeterminate form, and how do you resolve it?
4. Can all limits be computed by substitution, or are there cases requiring special techniques like L'Hôpital's Rule?
5. How does continuity affect the evaluation of limits?

**Tip:** When limits yield indeterminate forms like \( \frac{0}{0} \), algebraic manipulation (factoring, rationalizing, etc.) can often help resolve the issue.

Does the limit lim (x -> 12) (sqrt(x+4) - 4)/(x^2 + (-15)*x + 36) exist?

Learn how to compute the limit lim (x -> 12) (sqrt(x+4) - 4)/(x^2 + (-15)*x + 36). This problem involves algebraic manipulation, simplifying indeterminate forms, and applying limit laws. Suitable for Grades 11-12 or Introductory Calculus.

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