課程名稱︰微積分甲上
課程性質︰系內必帶
課程教師︰陳宏
開課學院：工學院
開課系所︰土木工程學系
考試日期（年月日）︰2009/9/29
考試時限（分鐘）：30min
是否需發放獎勵金：是，謝謝
（如未明確表示，則不予發放）
試題 :
Make sure to give sufficient reason in each problem or you will NOT get any
credit for your answer.
A. Determine whenever the following limits exist. Evaluate the limit if it
exists and explain why if not.
x-1
(a) (4 points) lim --------- √(x)表根號x
x→1 √(x)-1
|x|
(b) (4 points) lim ----------
x→0 |x+1|-1
(c) (4 points) lim (√(9x^2+x)+3x) √(9x^2+x)表根號(9^x2+x)
x→-∞
Hint. The identity (a-b)(a+b)=a^2-b^2 may be useful.
Hint. √(x^2)≠x
B. (8 points) Find all values of the constant c such that the function
f(x)={ cx^2+2x if x<π
x^3-cx if x>=π >=表大於等於
is continuous on (-∞,∞).
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