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研究所、轉學考(插大)-高等微積分
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104年 - 104 淡江大學 轉學考 高等微積分#55495
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題組內容
2(10%) Let a
1
± = 1 and a
n+1
=
for n = 1,2,3,...
(a) Show that a
n
is monotone increasing (by induction).
其他申論題
1.
#208992
2.
#208993
II. Traduzca las siguientes frases al espanol. ( 40% ) 最近的食品醜聞影響了台灣的油品市場。政府命令數以千計的產品下架，加強安全檢驗並降 低豬油關稅。這些進口豬油大部分來自西班牙。 面對自越南、香港和其他地區進口不宜食用豬油的疑慮以及大企業豬油商品下架等問題，台 灣對進口商品將嚴格把關並提高安檢層級。
#208994
【已刪除】1(10%) A sequence {xn} in is said to be a Cauchy sequence in case for every ε ＞ 0, there is a natural number n0 such that for all m,n＞ n0, then |xm — xn |＜ ε. Show that a convergent sequence is a Cauchy sequence.
#208995
(b) Show that an is bounded above by 2 (by induction).
#208997
(c) Find the limn→∞ an.
#208998
【已刪除】3(10%) is open or give a counterexample.
#208999
4(10%) Test for convergence or divergence
#209000
5(10%) Classify the following series into absolute convergence, conditional convergence or divergence. Explain why.
#209001
(a) Give the definition of uniform continuity of a function f defined on a set E .
#209002
for n = 1,2,3,...
for n = 1,2,3,...
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for n = 1,2,3,...