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研究所、轉學考(插大)-高等微積分
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110年 - 110 國立清華大學碩士班考試入學試題_數學系:高等微積分#105486
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4. (10%) Show that the function f : R
2
→ IR
2
defned by
has a fixed point.
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貳、應用文（佔 40 分） 某鄉（鎮區）農會為宣導農委會所推廣之「農地銀行」政策，以有效使用農地，活化農村人力，將舉辦三場「小地 主大佃農」之說明會。請您以農會業務辦理人之身分擬一份公文予各農事小組，通知農友踴躍參加，並廣為宣傳。 有意願配合此一政策者，會後得以當場索取相關辦法及申 請書。 （活動舉辦之日期、時間、地點、附件及相關內容皆請自訂。）
#448331
1. (10%) Calculate
#448332
2. (10%) Calculate the line integral where C is the positive oriented curve in R2-{(0,0)} parametrized by
#448333
3. (10%) Determine if converges uniformly on [-π,π].
#448334
5.(10%) Show that the set is compact.
#448336
6. (10%) Let X be a topological space andbe compact subsets. Is A U B always a compact set? Prove or give a counterexample.
#448337
7. (10%) Let f :R3 →R be a function defined by for(x，y，z) . Can f be extended to a differentiable function on R3?
#448338
(a) (10%) Is the family equicotinuous on [0,π ]?
#448339
(b) (10%) Does the sequence have a convergent subsequence?
#448340
(c) (10%) Is the familycompact?
#448341
has a fixed point.
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has a fixed point.