Limit Evaluation E27D5F
1. **State the problem:** Find the limit $$\lim_{x \to 2} \frac{3x^2 - 3x}{x - 0}$$.
2. **Rewrite the expression:** The limit is $$\lim_{x \to 2} \frac{3x^2 - 3x}{x}$$.
3. **Simplify the numerator:** Factor out 3x from the numerator:
$$3x^2 - 3x = 3x(x - 1)$$.
4. **Rewrite the limit:**
$$\lim_{x \to 2} \frac{3x(x - 1)}{x}$$.
5. **Simplify the fraction:** Cancel $x$ in numerator and denominator (for $x \neq 0$):
$$\lim_{x \to 2} 3(x - 1)$$.
6. **Evaluate the limit:** Substitute $x = 2$:
$$3(2 - 1) = 3 \times 1 = 3$$.
**Final answer:** $$3$$.