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研究所、轉學考(插大)-高等微積分
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110年 - 110 國立中山大學碩士暨碩士專班招生考試_應數系碩士班/丙組:高等微積分#104293
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1. (10 points) Is
=R? State your reason.
其他申論題
四、短文寫作（30 分。請以通行之散文體寫作，文長在 400-600 字之間，須分段，並加標點符號。） 題目：我想當一位華語教師 人生有許多轉折，也許原本想進企業界，卻走上了教育路；也許本來想自行創業，卻又轉回來想當教師。請敘寫你為何踏上華語教師之路。
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(1)突然／忽然
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(2)後來／然後
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2.語言教學原則強調「結構、功能、文化」之結合。請以「道歉」為主題，運用上述原 則於初級成人學生之華語口語能力的教學課程設計上，並說明你的教學重點為何？（15 分）
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2. (10 points) Show that = 1.
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3. (15 points) Is uniformly continuous on R? Prove your assertion.
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4. (15 points) Show that is a differentiable function on R. Is x =0 the derivative f':R→R a continuous function?
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5. (20 points) Show thatdx converges conditionally.
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6. (10 points) Let fn:[0,1] →R, , be a sequence of increasing functions, i.e., fn(x) ≤fn(y) for all and n N. Assume that fn Sfnt1 and Ifn(x)I s 1 for all xe [0,1] and neN. Show that fn converges (pointwisely) to an increasing function.
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7. (10 points) Can you find a C1 function f:R2 →IR such that Vf(x,y)= (-y,x) for all (x,y)? Find such a function or prove that it does not exist.
#441519
=R? State your reason.
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=R? State your reason.