推 demon1375 : 已存入共同必修 12/12 13:19
課程名稱︰微積分甲上
課程性質︰大一必修
課程教師︰朱樺
開課學院：工學院
開課系所︰材料系、電機系
考試日期（年月日）︰2014/10/6
考試時限（分鐘）：20 min
試題 :
CALCULUS QUIZ 1
Instructor: Professer Huah Chu
Quiz date: October 6, 2014
Quiz time: 20 minutes
Total score: 21 points (Each problem is worth 7 points)
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1.
(1+tanx)^(1/2)-(1+sinx)^(1/2)
Evaluate lim --------------------------------
x→0 x^3
(Do NOT use l'Hospital's Rule to solve this problem.)
2.
5^x+4^(-x)
Find all asymptotes of f(x) = ---------------
5^x-4^(-x)
3. Let f be a continious function with domain [1,3] and range
is [7,11]. Show that there exists c ∈[1,3] such that
f(c) = 2c+5.
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