課程名稱︰微積分甲上
課程性質︰必修
課程教師︰周青松
開課學院：理學院
開課系所︰數學系
考試日期（年月日）︰2014.7.3
考試時限（分鐘）：50
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
(1) Decide whether the following limits exist or not. Evaluate the values if
they exist.
(a) (20pt)
lim sin(x+π/3)-1
x→π/6 --------------
x-π/6
(b) (20pt)
f(x)=x^2-4x
lim f(x)-f(2)
x→4 ---------
x-3
(c) (20pt)
lim f(x)
x→4
x^2 , x<4
where f(x)= 15 , x=4
3x+4 , x>4
(2) For what values of A is the following f continuous at x=2? (20pt)
f(x)= A^2x^2 , x≦2
(1-A)x , x>2
(3) Set f(x)= x^2-x , x≦2
2x-2 , x>2
(a) Show that f is continunous at x=2.
(b) Determine the exitence of f'(2). (Use the definition of derivatives.)
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n > 2, X,Y,Z∈N, X^n + Y^n ≠ Z^n
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※ 編輯: yushenlin (140.112.245.186), 08/12/2014 14:11:18