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

(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%)

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.