We are given the expression \( \lim_{x \to 3} (x^2 - x) = 6 \), and we want to evaluate whether the limit holds.

### Step 1: Verify if \( x^2 - x = 6 \) when \( x = 3 \)
Substitute \( x = 3 \) into the expression \( x^2 - x \):

\[
x^2 - x = 3^2 - 3 = 9 - 3 = 6
\]

Indeed, \( x^2 - x = 6 \) when \( x = 3 \).

### Step 2: Take the limit
Since \( x^2 - x \) is a continuous function, we can directly substitute \( x = 3 \) into the expression:

\[
\lim_{x \to 3} (x^2 - x) = 3^2 - 3 = 9 - 3 = 6
\]

Thus, the limit is:

\[
\boxed{6}
\]

Let me know if you'd like further details or clarifications. 

Here are 5 related questions to practice:
1. What is \( \lim_{x \to 2} (x^2 - x) \)?
2. How do you evaluate \( \lim_{x \to 4} (x^2 - 2x + 1) \)?
3. What happens if you evaluate \( \lim_{x \to 0} (x^2 - x) \)?
4. Find \( \lim_{x \to 5} (x^2 - 2x) \).
5. How do you handle limits with discontinuous functions?

**Tip:** When evaluating limits for polynomial functions, substituting the value directly often works, as polynomials are continuous everywhere.

Explore how to evaluate the limit of the polynomial function x^2 - x as x approaches 3, including detailed steps and substitution. This problem introduces the concepts of limits and continuous functions, suitable for high school students in Grades 10-12.

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