Nilai \( \displaystyle \lim_{x \to 3} \ \frac{(x-2)^2-1}{x-3} = \cdots \)
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(EBTANAS SMA IPS 1999)
Pembahasan:
\begin{aligned} \lim_{x \to 3} \ \frac{(x-2)^2-1}{x-3} &= \lim_{x \to 3} \ \frac{(x^2-4x+4)-1}{x-3} \\[8pt] &= \lim_{x \to 3} \ \frac{x^2-4x+3}{x-3} \\[8pt] &= \lim_{x \to 3} \ \frac{(x-1)(x-3)}{x-3} \\[8pt] &= \lim_{x \to 3} \ (x-1) \\[8pt] &= 3-1=2 \end{aligned}
Jawaban C.