Evaluate `lim_(x to 3) (x^(7) - 2187)/(x^4 - 81)`

Explanation

To evaluate the limit \( \lim_{x \to 3} \frac{x^7 - 2187}{x^4 - 81} \), we can follow these steps:

### Step 1: Identify the limit form
First, we substitute \( x = 3 \) into the expression:
\[ \frac{3^7 - 2187}{3^4 - 81} \]
Calculating \( 3^7 \) gives \( 2187 \) and \( 3^4 \) gives \( 81 \). Thus, we have:
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