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︰地質科學系 生物環境系統工程系 生物產業機電工程系 工管系科管組
考試日期（年月日）︰103/12/26
考試時限（分鐘）：50分鐘
試題 :
(1) (20 pts)
Sketch the region Ω bounded by y = cosx, y = x+1, x = 1/2π
and find the volume of the solid generated by revolving this region
about the x-axis by using Washer method.
(2) (20 pts)
Sketch the regionΩ bounded by x = |y| and x = 2-y^2 and find the
volume of the solid generated by revolving this region about the y-axis
by using the shell method.
(3) (30 pts) Evaluate
(a) ∫e^2 1/x dx
e
(b) ∫e (ln x)/x dx
1
(4) (30 pts) Set f(x) = e^(-x^2)
(a) What is the symmetry of the graph?
(b) On what intervals does the function increase? decrease?
(c) What are the extreme values of the function?
(d) Determine the concavity of the graph and find the points of inflection.
(e) What is the horizontal asymptote of the graph?
(f) Sketch the graph.