Nilai \( \displaystyle \lim_{x \to 5} \ \frac{2x^3 - 20x^2 + 50x}{\sin^2 (x-5) \cos (2x-10)} = \cdots \)
- 0
- 1
- 5
- 10
- ∞
(SPMB 2006)
Pembahasan:
\begin{aligned} \lim_{x \to 5} \ \frac{2x^3 - 20x^2 + 50x}{\sin^2 (x-5) \cos (2x-10)} &= \lim_{x \to 5} \ \frac{2x \ (x^2 - 10x + 25)}{\sin^2 (x-5) \cos (2x-10)} \\[8pt] &= \lim_{x \to 5} \ \frac{2x \ (x-5)(x-5)}{\sin^2 (x-5) \cos (2x-10)} \\[8pt] &= \lim_{x \to 5} \ \frac{(x-5)(x-5)}{\sin^2 (x-5) } \cdot \lim_{x \to 5} \ \frac{2x}{\cos (2x-10)} \\[8pt] &= (1)^2 \cdot \frac{2(5)}{\cos 0} = 1 \cdot \frac{10}{1} = 10 \end{aligned}
Jawaban D.