課程名稱︰微積分乙上
課程性質︰系定必修
課程教師︰李聰成
開課學院：管院
開課系所︰數學系
考試日期（年月日）︰2009/01/15
考試時限（分鐘）：(10:20~1:00)
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
請將每一步驟表達清楚, 不可以只寫答案
1. Evaluate the indefinite integral(不定積分).
__
cos√t
∫--------- dt
__
√t
2. Find the area(面積) of the region(區域) enclosed by the curves y=sinx,
y=cos2x, x=0, and x=π/2.
3. Evaluate the limit.
n π iπ
lim Σ ---- tan -----
n→+∞ i=1 4n 4n
4. Evaluate the definite integral(定積分).
2 1
∫ _ ----------------- dt
√2 ______
t^3 √t^2 -1
5. Find the value of the positive constant c such that
x+c
lim (-----)^x =9
n→+∞ x-c
6. Find the volume(體積) of a right circular cone(圓錐) with height h and
base radius γ.
7. Find an equation for the tangle line to the curve y=e^x that passes
through the origion(原點).
8. Use logarithmic differentiation to find the derivative of the function
(sinx)^2 (tanx)^4
y = --------------------
(x^2 + 1)^2 ,
where x € (0,π/2) (我找不到屬於的符號/3\bbb)
9. Show that
x ______
ƒ(x)=∫ √1+t^3 dt
1
is one-to-one on (-1,+∞) and find (ƒ^-1)'(0).
10. Evaluate the limit.
x 1
lim (----- - ------)
n→1+ x-1 ㏑x
其實期末考題都在老師勾的習題裡啦…作課本比較實際。
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