Nilai lim_(x→3)⁡(x-3)(√x+√3)/(√x-√3)=⋯

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Bahas Soal Matematika   »   Limit   ›  

Nilai \( \displaystyle \lim_{x \to 3} \ \frac{(x-3)(\sqrt{x}+\sqrt{3})}{\sqrt{x}-\sqrt{3}} = \cdots \)

  1. 0
  2. 3
  3. 6
  4. 12
  5. 15

(SPMB 2004)

Pembahasan:

\begin{aligned} \lim_{x \to 3} \ \frac{(x-3)(\sqrt{x}+\sqrt{3})}{\sqrt{x}-\sqrt{3}} &= \lim_{x \to 3} \ \frac{(\sqrt{x}-\sqrt{3})(\sqrt{x}+\sqrt{3})(\sqrt{x}+\sqrt{3})}{\sqrt{x}-\sqrt{3}} \\[8pt] &= \lim_{x \to 3} \ (\sqrt{x}+\sqrt{3})(\sqrt{x}+\sqrt{3}) \\[8pt] &= (\sqrt{3}+\sqrt{3})(\sqrt{3}+\sqrt{3}) \\[8pt] &= (2\sqrt{3}) (2\sqrt{3}) = 4 \cdot 3 \\[8pt] &= 12 \end{aligned}

Jawaban D.