Nilai \( \displaystyle \lim_{x \to q} \ \frac{x\sqrt{x}-q\sqrt{q}}{\sqrt{x}-\sqrt{q}} = \cdots \)
- \( 3 \sqrt{q} \)
- \( \sqrt{q} \)
- \( q \)
- \( q \sqrt{q} \)
- \( 3q \)
(SPMB 2005)
Pembahasan:
\begin{aligned} \lim_{x \to q} \ \frac{x\sqrt{x}-q\sqrt{q}}{\sqrt{x}-\sqrt{q}} &= \lim_{x \to q} \ \frac{x\sqrt{x}-q\sqrt{q}}{\sqrt{x}-\sqrt{q}} \times \frac{\sqrt{x}+\sqrt{q}}{\sqrt{x}+\sqrt{q}} \\[8pt] &= \lim_{x \to q} \ \frac{x^2+x\sqrt{qx}-q\sqrt{qx}-q^2}{x-q} \\[8pt] &= \lim_{x \to q} \ \frac{(x-q)(x+q)+\sqrt{qx}(x-q)}{x-q} \\[8pt] &= \lim_{x \to q} \ (x+q)+\sqrt{qx} \\[8pt] &= (q+q) + \sqrt{q^2} = 2q + q \\[8pt] &= 3q \end{aligned}
Jawaban E.