Subjects calculus

Limit Evaluation E27D5F

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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:** $$3$$.