Nilai \( \displaystyle \lim_{x \to 1} \ \frac{x-1}{\sqrt{x+3}-2} = \cdots \)
- 1/4
- 1/2
- 1
- 2
- 4
(SPMB 2007)
Pembahasan:
\begin{aligned} \lim_{x \to 1} \ \frac{x-1}{\sqrt{x+3}-2} &= \lim_{x \to 1} \ \frac{x-1}{\sqrt{x+3}-2} \times \frac{\sqrt{x+3}+2}{\sqrt{x+3}+2} \\[8pt] &= \lim_{x \to 1} \ \frac{(x-1)(\sqrt{x+3}+2)}{(x+3)-4} \\[8pt] &= \lim_{x \to 1} \ \frac{(x-1)(\sqrt{x+3}+2)}{x-1} \\[8pt] &= \lim_{x \to 1} \ (\sqrt{x+3}+2) \\[8pt] &= \sqrt{1+3}+2 = 4 \end{aligned}
Jawaban E.