To solve the limit:

\[
\lim_{x \to 13} \frac{\sqrt{x+3} - 4}{3x - 39}
\]

### Step 1: Direct Substitution
First, attempt direct substitution by plugging \( x = 13 \) into the expression.

\[
\frac{\sqrt{13 + 3} - 4}{3(

Learn how to solve the limit lim x->13 ((sqrt(x+3)-4)/(3x-39)) with step-by-step guidance. This problem explores algebraic manipulation, square roots, and applying the conjugate method to simplify complex limits. Ideal for students in Grades 11-12.

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