3. (10%) Show that lim_x→0 x² sin = 0.

(a)

(b)

5. (15%) Sketch the graph of

(a) x(2 + x5) dx

(b) dx

7. (10%) The region R enclosed by the curves y = x and y = x2 is rotated about the x-axis. Find the volume of the resulting solid.

8. (15%) A group of engineers is building a parabolic satellite dish whose shape will be formed by rotating the curve y = ax2 about the y-axis. If the dish is to have a 10-ft diameter and a maximum depth of 2 ft, find the value of a and the surface area of the dish.

一、英翻中 (50%)  1. 摘錄自 Translaboration: Exploring collaboration in translation and translation in collaboration (178 words, 灰色處人名不用翻譯)   The fusion of translation and collaboration creates a 'translaboration', a so-called "blended concept" (Fauconnier and Turner 2002). Collaboration has made considerable inroads into Translation Studies in recent years, joining Translation Studies' central concept of 'translation' in investigations of the various types of collaborative translation occurring in both the offline and the online realms. The time is therefore ripe for the two concepts to converge, as they share many commonalities and have experienced a certain common fate, as will be shown in this introduction and the various contributions to this special issue of Target. The contributions collected here all focus on the specific meanings and facets of translaboration, as laid out in this introduction, and in doing so add new meanings and layers to the concept. The contributors all deal with the concept of translaboration in relation to their own specific themes and contexts, and together the individual contributions and this introduction cover an astounding spectrum of applications of this blended concept - a concept with well-defined contours, but a core that is still in the making.

2. 摘錄自 “Taiwan most democratic country in East Asia: The Economist" (117 words) Taiwan is the most democratic country in East Asia and No. 11 in the world, according to the annual Democracy Index published by The Economist Intelligence Unit (EIU經濟學人智庫) Tuesday (Feb. 2). The Economist explained that "The pandemic caused an unprecedented rollback of democratic freedoms in 2020." The report divided 167 countries into four categories: authoritarian regimes, hybrid regimes, flawed democracies, and full democracies. While Taiwan was still categorized as a "flawed democracy" in 2019, transparency in political party financing, as well as political and judicial reforms, propelled the nation 20 places higher on the current list, CNA reported. Taiwan was also one of only 38 countries to improve their ranking in 2020 compared to the previous year.

二、中翻英 (50%) Translate the highlighted text into English (Source: https://talk.ltn.com.tw/article/paper/1426483). 社論》「罷王」案通過之後的省思 桃園市議員王浩宇遭罷免,成為直轄市議員的首例,連日來引發諸多議論。一位知名度甚高的 政治人物被選民否定,有其個人肇因,也有大環境因素;且因下月初還有高雄市議員黃捷罷免 案投票,其政治效應乃廣受矚目,即所謂「報復性罷免」或將接踵而至,甚至預示明年縣市長選舉的趨勢。 王浩宇創紀錄地遭罷除,最主要是其個人表現。他不但不畏言行爭議,還屢從爭議所帶來的網 路聲量打造個人知名度,以致有「全國不分區議員」封號。在此過程,他到處開闢戰場,多方 出征,幾乎得罪了政壇上大小政黨,甚至還被質疑有辱及賽德克族的言論。同時,他曾棄綠黨 而轉戰民進黨,在議員的本職表現也被質疑,曾數度被移送議會紀律委員會,家人擁有非法農 舍也不利形象。王浩宇的挫敗,對現今一味追求網路聲量的政治人物和政黨,無疑是一大教訓; 長期而言,政治雖總有民粹的成分,仍須顧及社會觀感和選民經營,不能本末倒置,甚至飲鴆止渴。 選區的選民結構也是關鍵因素。在藍大於綠的中壢選區,於綠營很出鋒頭的年輕議員,卻成為 藍營眾矢之的,還匯集了各方「報復」的力量;尤其對當事人去年在罷免韓國瑜市長案的怨氣, 加上最近美豬議題發酵,都是「罷王」案通過的重要相關因素。正因如此,在市議員的複數選 區選制下,儘管罷免案通過的門檻甚高,所需票數是王浩宇當選票數的五倍,仍以投票率二十 八,一%,且同意票高於門檻二六四二票過關。 投票數字在政治上凸顯了動員的結果。正就美豬議題無限上網的中國國民黨,無疑把「罷王」 案當成炒作這一議題的練兵場,「大砲打小鳥」,以圖為擬議中的「罷萊菜委」及八月反美豬公 投案添加柴火。同時,王浩宇近年多所得罪的大小政黨,也經主其事的公民團體奔走連繫,先 後以個人或政黨加入助陣。在各方「圍攻」之下,個人網路聲量再高,也難敵主動及被激發動 員而走進投票所的選民數。 另外,從選舉趨勢看,這也是選罷法四年多前修正,降低罷免案通過的門檻為「同意票數大於 不同意票數,且同意票數達原選舉區選舉人總數四分之一以上」,並延長連署時間,刪除禁止 宣傳規定等的必然發展。僅在過去一年間,就有十幾件包括直轄市長、議員、鄉鎮市民代表、 村里長的罷免案提出或投票。這一方面是前此各種選舉恩怨及地方利益的衝突,主要仍是罷免 规定松绑的結果,預料罷免案如雨後春筍出現的這種情況,勢將持續。 

115年 - 115 中央警察大學_碩士班入學考試試題_海洋科技組：微積分#139855

115年 - 115 中央警察大學_碩士班入學考試試題_消防科學研究所、交通管理研究所：微積分#139760

114年 - 114 臺灣綜合大學系統_學士班轉學生考試試題:微積分A#137897

114年 - 114 臺灣綜合大學系統_學士班轉學生考試試題：微積分B#137819

114年 - 114 台灣聯合大學系統_學士班轉學生考試試題:微積分#137762

114年 - 114 台灣聯合大學系統_學士班轉學生考試試題:微積分#137761

114年 - 114 國立臺灣大學_轉學生招生考試_物理學系/土木工程學系/生物環境系統工程學系/生物機電工程學系:微積分(B)#137745

114年 - 114 國立臺灣大學_轉學生招生考試_數學系:微積分(A)#137744

113年 - 113 國立嘉義大學_轉學生招生考試試題_(全校)：微積分#122986

112年 - 112 國立臺灣大學_碩士班招生考試題：微積分(D)#130254