[轉錄][試題] 96上 黃漢水 微積分甲上 期中考
課程名稱︰微積分甲(上)
課程性質︰系定必修
課程教師︰黃漢水
開課學院：生機、生工、地質、工管
開課系所︰數學系
考試日期（年月日）︰2007/11/19
考試時限（分鐘）：170分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
一 Find the following limits if it exist: (18％)
________
(1)lim {[2/(x+3)]-1}/(x^2-1) (2) lim (√1/(t+12)-1/4)/(t^2-16)
x→-1 ________ ________ t→4
(3)lim √x^2+5x+3-√x^2+2x-2
x→-∞
二 (1)Sketch the graphs of the function f(x)=(x+2)/x^(1/3)
(2)Find the absolutely maximum value and the absolutely minimum value
of f(x) on the closed interval [0.001,8]
(3)Find the absolutely maximum value and the absolutely minimum value
of f(x) on the closed interval [-8,-0.001]
(15％)
三 (1)Sketch the graphs of the function g(x)=x^3/(x^2-3)
(2)Find the absolutely maximum value and the absolutely minimum value
of g(x) on the closed interval [-1,1]
(3)Find the absolutely maximum value and the absolutely minimum value
of g(x) on the closed interval [2,5]
(15％)
四 Let h(x)=x^2+3x+2 Find all tangent lines from the point (1,5)
to the curve y=h(x) (20％)
五 The curve y=ax^2+bx+c passes through the point (1,0)
Suppose that y=5x-7 is the tangent line of the curve at the point
(2,3) Find a, b and c (20％)
六 Suppose that g(x) is a function such that (12％)
(1) g(x) is continuous on [1,4]
(2) g`(x) exits for any 1<x<4
(3) g``(x)<0 for any 1<x<4
(4) g(1)=g(4)=3
Prove that g(x)>3 for any 1<x<4
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※ 編輯: ken2002cool 來自: 219.81.153.112 (11/03 21:47)
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