Nilai lim_(x→q)⁡ (x√x-q√q)/(√x-√q)=⋯

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Website Belajar Matematika & Statistika

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Bahas Soal Matematika   »   Limit   ›  

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

  1. \( 3 \sqrt{q} \)
  2. \( \sqrt{q} \)
  3. \( q \)
  4. \( q \sqrt{q} \)
  5. \( 3q \)

(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.