课程名称︰微积分甲上
课程性质︰必修
课程教师︰周青松
开课学院：理学院
开课系所︰地质科学系 生物环境系统工程系 生物产业机电工程系 工管系科管组
考试日期（年月日）︰103/12/26
考试时限（分钟）：50分钟
试题 :
(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.