$\lim_{x \to 1} \frac{x^4 - 1}{x - 1} - \lim_{x \to 2} \frac{x^3 - 4x^2 + 4x}{x^2 - 4}$
Step-by-Step Solution
Key Concept: First limit: $(x^4 - 1)/(x - 1) = x^3 + x^2 + x + 1 \to 4$. Second: factor $x^3 - 4x^2 + 4x = x(x - 2)^2$ and $x^2 - 4 = (x - 2)(x + 2)$; ratio $\to 2(0)/4 = 0$. Result $= 4 - 0 = 4$.
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Correct Answer: (3)