4. Evaluate , where R is the region bounded by x + y = 0, x + y = 1, x - y = -1, and x - y = 2.
3. Use Lagrange Multiplier method to calculate the maximum value of x + 2y subject to the condition that ≤ 1.
2. Suppose that the function y(x) satisfies the following differential equation: = y(x)(1 - y(x)). If y(0) =, then find y(2).
(Hint: separation of variables)
2.
The most exciting kind of education is also the most personal. Nothing can exceed the joy of discovering for yourself something that is important to you. It may be an idea or a bit of information you come across accidentally or a sudden insight, fitting together pieces of information or working through a problem. Such personal encounters are the "payoff" education. A teacher may direct you to learning and even encourage you in it-but no teacher can make the excitement or the joy happen. That's up to you.
A research paper, assigned in a course and perhaps checked at various stages by an instructor, leads you beyond classrooms, beyond the texts for classes and into a process where the joy of discovery and learning can come to you many times. Preparing the research paper is an active and individual process, and ideal learning process. It provides a structure within which you can make exciting discoveries, of knowledge and of self, that are basic to education. But the research paper also gives you a chance to individualize a school assignment, to suit a piece of work to your own interests and abilities, to show others, what you can do. Writing a research paper is more than just a classroom exercise. It is an experience in searching out, understanding and synthesizing, which forms the basis of many skills applicable to both academic and nonacademic tasks. It is, in the, fullest sense, a discovering, an education. So, to produce a good research paper is both a useful and a thoroughly satisfying experience.
To some, the thought of having to write an assigned number of pages often more than ever produced before, is disconcerting. To others, the very idea of having to work independently is threatening. But there is no need to approach the research paper assignment with anxiety, and nobody should view the research paper as an obstacle to overcome. Instead, consider it a goal to accomplish, a goal within reach if you need the help this book can give you.
40. What will probably follow this passage?
(A) How to write a research paper.
(B) The importance of research in education.
(C) How to make new discoveries for oneself.
(D) The skill of putting pieces of information together.
39. The writer argues in the passage that_____________.
(A) one should explore new areas in research
(B) one should trust one's own ability to meet course requirements
(C) one should consider research paper writing a pleasure, not a burden
(D) one should use all one's knowledge and skills when doing research
38. From the context, the word "disconcerting" (Para.3) most probably means_____________.
(A) misleading
(B) embarrassing
(C) stimulating
(D) upsetting
This is a large modal.