Nilai \( \displaystyle \lim_{x \to 5} \ \frac{(4x-10) \sin (x-5)}{x^2-25} = \cdots \)
- -3
- -1
- 1
- 2
- 4
(EBTANAS SMA IPA 1998)
Pembahasan:
\begin{aligned} \lim_{x \to 5} \ \frac{(4x-10) \sin (x-5)}{x^2-25} &= \lim_{x \to 5} \ \frac{(4x-10) \sin (x-5)}{(x-5)(x+5)} \\[8pt] &= \lim_{x \to 5} \ \frac{(4x-10)}{(x+5)} \cdot \lim_{x \to 5} \ \frac{\sin (x-5)}{(x-5)} \\[8pt] &= \frac{4(5)-10}{5+5} \cdot 1 = \frac{20-10}{10} = \frac{10}{10} \\[8pt] &= 1 \end{aligned}
Jawaban C.