Nilai \( \displaystyle \lim_{x \to 1} \ \frac{(x-1)(\sqrt{x}+1)}{(\sqrt{x}-1)} = \cdots \)
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(SPMB 2007)
Pembahasan:
\begin{aligned} \lim_{x \to 1} \ \frac{(x-1)(\sqrt{x}+1)}{\sqrt{x}-1} &= \lim_{x \to 1} \ \frac{(x-1)(\sqrt{x}+1)}{\sqrt{x}-1} \times \frac{\sqrt{x}+1}{\sqrt{x}+1} \\[8pt] &= \lim_{x \to 1} \ \frac{(x-1)(\sqrt{x}+1)^2}{x-1} \\[8pt] &= \lim_{x \to 1} \ (\sqrt{x}+1)^2 \\[8pt] &= (\sqrt{1}+1)^2 = 4 \end{aligned}
Jawaban D.