2017年广西桂林电子科技大学数学专业英语考研真题A卷.doc

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2017 年广西桂林电子科技大学数学专业英语考研真题 A 卷英译汉 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 only 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 and element not in the other, we say the sets are unequal and we write A B . 5. Theorem 1. A monotonic sequence converges if only if it is bounded. Note: A sequence { ( )} f n is called bounded if there exists a positive number M such that | ( ) | M foralln. f n  A sequence that is not bounded is called unbouned. Proof: It is clear that an unbounded sequence cannot converge. Therefore, all we need to prove is that a bounded monotonic sequence must converge. Assume values. Then ( ) f n  and let L denote the least upper bound of the set of function ( ) L f n  for all n, and we shall prove that the sequence converges to L.

Choose any positive number . Since L  ( ) f N ( ) f n , we must have all numbers L   cannot be an upper bound for for some N. … From these inequalities we find that 0 L-f(n)<  for all n N and this means that the sequence converges to L, as asserted. ( ) f n  , the proof is similar, the limit in this case being the greatest low If bound of the set of function values.

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2017年广西桂林电子科技大学数学专业英语考研真题A卷.doc

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