课程名称︰微积分乙上
课程性质︰必修
课程教师︰张志中
开课学院：
开课系所︰牙医系 药学系 医技系 物治系 职治系 农化系 公卫系
考试日期（年月日）︰2018/11/1
考试时限（分钟）：50
是否需发放奖励金：是
试题 :
1. (20 points) Evaluate the following limits.
(a)
cos(x)-cos(3x)
lim ———————
x→0 3x^2
(b)
x^2-(π^2)/4
lim ———————
x→π/2 sin(cos(x))
2. (40) Answer the following questions and sketch the graph
x^2-49
of y = f(x) = ———————
x^2+5x-14
(a) What is the domain of definition of the function?_______________,
(b) Is there a removable discontinuity? Where is it(if any)?________,
(c) Evaluate f'(x)=_________________________________________________,
(d) Evaluate f"(x)=_________________________________________________,
(e) f(x) is increasing on the interval(s):__________________________,
(f) f(x) is concave upward on the interval(s):______________________,
(g) f(x) has (none, one or several) local maximum at (x,y)=_________,
and (none, one or several) local minimum at (x,y)=______________,
(h) f(x) has inflection point(s) at (x,y)=(if any)__________________,
(i) f(x) has asymptote(s) (if any)__________________________________,
(j) Sketch the graph of y=f(x).