15. Find the arc length __⑮__ of the curve x = a cos³ θ and y = a sin³ θ on the interval [0, 2π].

16. Find the area __⑯__ of the triangle with the given vertices A(0, 0, 0), B(1, 0, 3), and C(-3, 2, 0).

17. Find the maximum value = __⑰__ of the directional derivative of w = xy²z² at P(2, 1, 1).

18. Find the maximum = __⑱__ of f(x, y, z) = xyz subject to constraints x + y + z = 32, x - y + z = 0, x ≥ 0, y ≥ 0, and z ≥ 0.

19. Evaluatexy dy dx =__⑲__

20. Find the volume __⑳__ of the solid is bounded by r² + z² = a² and r = a cos θ.

1. 語句修繕 (5%): 請將以下機器翻譯出來的語句，改寫成語法正確、表達通順的中文。       「我最近了解到這個詞叫做『躺平』(quiet quitting)，意思是你不是徹底辭職，而是放棄超越自我的想法，」擁有超過 10,000 名粉絲的 TikTok 用戶 Zaiad Khan 在一次採訪中說，舒緩的聲音，與紐約市地鐵的視頻並列。「你仍在履行你的職責，但你不再在精神上認同工作必須是我們生活的那種忙碌文化。」

2. 換句話說 (5%):依照前一題對於「躺平」的定義，請您寫出五個「躺平」的同義詞，並依照語域高低，由高至低排列。

3. 翻譯評論 (10%): 以下英文段落出自十九世紀英國作家勃朗特 (Charlotte Brontë, 1816-1855) 長篇小說《簡愛》(Jane Eyre, 1847) 第八章，中文翻譯則分別出自一九三五年的伍光建譯本和一九三六年的李霽野譯本，請您仔細比較過後評論這兩個譯本的特色，並說明您偏好伍光建或李霽野的翻譯。 That night, on going to bed, I forgot to prepare in imagination the Barmecide supper of hot roast potatoes, or white bread and new milk, with which I was wont to amuse my inward cravings: I feasted instead on the spectacle of ideal drawings. (Brontë, 1847) 我向來最喜歡吃烤薯, 白麵包, 新鮮牛奶, 上床時總想到這幾件好吃的東西, 現在卻不然了； 我臨睡的時候, 所想的都是繪畫。(伍光建, 1935) 那一晚上床睡覺的時候, 平常我愛拿來滿足我內心渴望的那種畫餅充飢的烤馬鈴薯或白麵包和新鮮牛奶的晚餐, 我忘記在想像中預備了, 我卻拿我暗中見到的空幻的畫景來做盛宴。(李霽野, 1936)

II. English Ability 1. Paraphrasing: Rewrite the following paragraph in English to express the same meaning or information with different wording and structure.  An Immense World by Ed Yong is a book filled with strange creatures and experiments； Yong is interested in what animals perceive and what they might communicate to us. Humans see the world one way, and other species see it through very different eyes, and many don't see it at all. Attempting to exchange one worldview-or, to use the term Yong favors, Umwelt--for another may be frustrating, but, he argues, that's what makes the effort worthwhile. It reminds us that, "for all our vaunted intelligence," our Umwelt is just one among millions. Some species of scallops, for instance, have dozens of eyes； others have hundreds. We can learn a lot from the methods that animals use to sense their surroundings. And doing so can be, for us, mind-expanding.

2. Summarizing: Write a summary in English between 50 to 80 words to get the gist of the following paragraphs. (It is strongly recommended not to copy the same sentences of the original texts.)  Of the character sketches that the English satirist Samuel Butler wrote in the mid-seventeenth century- among them "A Degenerate Noble," "A Huffing Courtier," "A Small Poet," and "A Romance Writer"-the most recognizable today is "A Modern Critic." He is a contemptible creature: a tyrant, a pedant, a crackpot, and a snob； "a very ungentle Reader"； "a Corrector of the Press gratis"； "a Committee-Man in the Commonwealth of letters"； "a Mountebank, that is always quacking of the infirm and diseased Parts of Books." He judges, and, if authors are to be believed, he judges poorly. He praises without discernment. He invents faults when he cannot find any. Beholden to no authority, obeying nothing but the mysterious stirrings of his heart and his mind, he hands out dunce caps and placards insolently and with more than a little glee. Authors may complain to their friends, but they have no recourse. The critic's word is law. Butler's sketch would still strike a chord with aggrieved writers today, but, in his time, the Modern Critic- part mountebank, part magician was a new phenomenon. The figure's shape-shifting in the centuries since is the subject of John Guillory's new book, "Professing Criticism" (Chicago), an erudite and occasionally biting series of essays on "the organization of literary study." Guillory has spent much of his career explaining how works of literature are enjoyed, assessed, interpreted, and taught； he is best known for his landmark work, "Cultural Capital" (1993), which showed how literary evaluation draws authority from the institutions principally universities within which it is practiced. To suggest, for instance, that minor poets were superior to major ones, as T. S. Eliot did, or that the best modernist poetry was inferior to the best modernist prose, as Harold Bloom did, meant little unless these judgments could be made to stick-that is, unless there were mechanisms for transmitting these judgments to other readers.

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