(i) range= __(6i) (2%)__

Ⅱ 、計算題(計算過程列入計分,並標註最後答案)7.If f(x)=(2014x6+2x+8)x,find f'(x).(5%)

8.if f(x)=dt,find f'(x). (5%)

9. Evaluate dx (5%)

10. Find to the 1-st decimal place by the Newton's method with an initial guess of x0 =4. (5%) 

Ⅲ、11. Calculatc the itegmdxdzdy (10%)

12. Find the volume of the given solid under the surface z = xy and above the triangle with vertices (1, 1), (4, 1), and (1, 2). (10%)

13. Find the volume of the parallelepiped determined by vectors a =i+ j-k, b=i-j+k, c=i+j+k. (10%)

14. Find the Maclaurin series of the function and its radius of convergence. (10%)

15. Evaluate the integral for by making an appropriate change of variables, where R is given by the inequality |xl+ly |≤1.(10%) 

Part A. Question Design (15%) Attention : You DON’T need to paraphrase or summarize the following passages. 1. Cloze (5 %) Directions : 1. Design a multiple-choice cloze test with FIVE blanks. Each question should have four answer options, with one correct answer and three distractors.2. Underline the part of speech if you want to leave it blank.3. Circle the correct answer to each question.       The Great Sphinx in the Giza desert is a mythological creature with the body of a lion and the head of a human being. This monumental statue is often regarded as a national symbol of Egypt, having guarded the famous Egyptian pyramids for 4,000 years. Nevertheless, the stone creature does not look like it did 4,000 years ago; wind, water, pollution, and human contact have slowly aged the rock. Scientists are now trying to restore it. They not only want it to look like it did when it was first built but also are looking for ways to keep it from deteriorating more than it has.      Fixing the Sphinx is not an easy job. It takes several years of planning before the work begins. Each stone in the Sphinx is carefully measured. Scientists use computers to help figure out the size and shape of each stone. Each old stone is given a number. Then, one by one, replacement stones are carved by hand, just like people did long ago, in the exact sizes and shapes as the ones they are replacing. When the new stones are ready, they are installed and the worn ones are removed.       Scientists are also worried about how to keep the Sphinx from falling apart again. However, there is no easy solution to the problem, not to mention a solution that is agreeable to all parties. The one thing that is agreed upon is that something needs to be done to protect this ancient sculpture.

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