作者cookie20125 (餅乾\⊙▽⊙/)
看板NTU-Exam
標題[試題] 104上 李聰成 微積分乙上 期末考
時間Fri Jan 15 23:30:57 2016
課程名稱︰微積分乙上
課程性質︰共同必修
課程教師︰李聰成
開課學院：管院
開課系所︰
考試日期（年月日）︰2016/01/14
考試時限（分鐘）：160分鐘
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 definite integral.
1 _____
∫ √1-x^2dx
0
2.Find the area (面積) of the region (區域) bounded by
the curves
y=2-x^2 , y=|x|
3.Evaluate the indefinite integral.
1
∫－－－－－dx
√(1+√x)
4.Evaluate the limit.
1 1
lim ( ------- - --- )
x→0 ln(x+1) x
5.Evaluate the limit.
n n n n
lim ( ———— + ———— + ———— + ...+ ———— )
n→+∞ n^2+1^2 n^2+2^2 n^2+3+2 n^2+n^2
6.Use logarithmic differentiation to find the derivative
of the function
(x^2+1)^3(2x-5)^2
y= ————————— , where x>3
(x^3+5)^2
7.Show that f is one-to-one on (0, +∞) and find an
equation of the tangent line (切線) to the graph of
y=f^-1(x) at x=4, where
________
f(x) = √x^3+2x+4
and f^-1 is the inverse function (反函數) of f.
8.Find the volume of the solid formed by revolving
(旋轉) the region (區域) bounded by the graphs of
y=x and y=x^2 in the first quadrant (象限) about
the y-axis.
9.Find values of a and b for which
sin2x+ax+bx^3
lim ——————— = 0
x→0 x^3
10.Find the extreme values of f(x)=x^x on (0, +∞).
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※ 編輯: cookie20125 (140.112.241.221), 01/15/2016 23:32:08