2017年廣西桂林電子科技大學(xué)數(shù)學(xué)專業(yè)英語考研真題A卷

1、2017年廣西桂林電子科技大學(xué)數(shù)學(xué)專業(yè)英語考研真題A卷英譯漢1.(1) straight line (2) even integer (3) positive number(4) x to the minus two thirds (5) complex-valued sequence (6) the second derivative 2. Before 17th century, man confined himself to the elementary mathematics, i.e., geometry, trigonometry and algebra, in which onl

2、y the constants were considered.3. A circle is a closed curve lying in one plane, all points of which are equidistant from a fixed point called the center. 4. Two sets A and B are said to be equal if they consist of exacly the same elements, in which case we write A=B. If one of the sets contains an

3、d element not in the other, we say the sets are unequal and we write .5. Theorem 1. A monotonic sequence converges if only if it is bounded.Note: A sequence is called bounded if there exists a positive number M such that A sequence that is not bounded is called unbouned. Proof: It is clear that an u

4、nbounded sequence cannot converge. Therefore, all we need to prove is that a bounded monotonic sequence must converge. Assume and let L denote the least upper bound of the set of function values. Then for all n, and we shall prove that the sequence converges to L.Choose any positive number . Since cannot be an upper bound for all numbers , we must have for some N. From these inequalities we find that for all and this means that the sequence converges to L, as asserted. If , the proof is similar, the limi