47. Which of the following can be inferred from the passage?
(A) The author believes that technological innovation has completely replaced human ability in elite sports.
(B) Spectators value measurable performance more than creativity.
(C) Artificial intelligence has eliminated uncertainty from sporting competitions.
(D) Public perceptions of fairness in sport are likely to evolve over time.

48. What is the primary function of Paragraph 6? (A) To argue that current technological controversies are historically unprecedented. (B) To criticize the use of electronic timing systems and video review. (C) To provide historical context suggesting that public resistance to technological change often diminishes over time. (D) To demonstrate that cognitive technologies have little influence on sport.

49. The author's attitude toward the increasing use of technology in sport is best described as __________ . (A) unequivocally supportive (B) strongly opposed (C) balanced and analytical (D) indifferent

50. Which statement would the author most likely agree with? (A) Athletic excellence should be defined exclusively by measurable performance outcomes. (B) Technological progress inevitably diminishes the value of human achievement. (C) Artificial intelligence should assume responsibility for strategic decision-making in all professional sports. (D) The future of sport depends not only on technological innovation but also on how society chooses to define excellence.

1. 極限 $\lim_{x \to 0} \frac{\sin x - x \cos x}{x^3}$ 之值為何？(A) $\frac{1}{6}$(B) $\frac{1}{3}$(C) $\frac{1}{2}$(D) 1

2. 函數 $e^x \cos x$ 在 $x = 0$ 的泰勒級數展開中，$x^4$ 的係數為何？(A) $-\frac{1}{6}$(B) 0(C) $\frac{1}{24}$(D) $\frac{1}{6}$

3. 設 $F(x) = \int_x^{x^2} e^{t^2} dt$ 則 $F'(1)$ 之值為何？(A) 0(B) $e$(C) $2e$(D) $-e$

4. 級數 $\sum_{n=1}^{\infty} (-1)^{n-1} \frac{n}{n^2+1}$ 的收斂性為下列何者？(A) 絕對收斂(B) 條件收斂(C) 發散，因為一般項非單調遞減(D) 發散，因為一般項不趨近於 0

5. 設 $D = \{(x, y) : 0 \leq y \leq x \leq 1\}$。試求 $\iint_D (x + y) dA$ 之值為何？(A) $\frac{1}{3}$(B) $\frac{1}{2}$(C) $\frac{2}{3}$(D) 1

6. 參數曲線 $\begin{cases} x = t^2 + 1 \\ y = t^3 - t \end{cases}, t \in \mathbb{R}$ 在 $t = 1$ 處的切線方程式為何？(A) $y = x - 2$(B) $y = 2x - 4$(C) $y = -x + 2$(D) $y = x + 2$

7. 求冪級數 $\sum_{n=1}^{\infty} \frac{(x-1)^n}{n^2}$ 的收斂區間。(A) $(-1,3)$(B) $[-1,3)$(C) $(-1,3]$(D) $[-1,3]$

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