If `lim_(x to 1) (x^(3) - 1)/(x - 1) = lim_(x to k) (x^(4) - k^(4))/(x^(3) - k^(3))`, find the value of k.

Explanation

To solve the problem, we need to evaluate both sides of the equation given in the limit and find the value of \( k \).

### Step-by-Step Solution:

1. **Evaluate the Left-Hand Side (LHS)**:
\[ \lim_{x \to 1} \frac{x^3 - 1}{x - 1} \]
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