课程名称︰微积分甲上
课程性质︰大一必修
课程教师︰朱桦
开课学院：工学院
开课系所︰材料系、电机系
考试日期（年月日）︰2014/11/3
考试时限（分钟）：30 min
试题 :
CALCULUS QUIZ 3
Instructor: Professor Huah Chu
Quiz date: November, 3 2014
Quiz time: 30 minuates
Total score: 21 points(Each problem is worth 7 points)
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1. Find
lim [(1+(1/x))^x-e]
x→∞
2. Let f and g be continuous and differentiable on (a,b). Suppose
(f'g - fg')(x) ≠0 for all x ∈(a,b). Show that beween two roots
of f(x) = 0 lies one roots of g(x) = 0. [Hint: Consider f/g]
3. Let f(x) = (e^x)(cosx), x ∈(0,2π)
(a) Find the intervals of increase or decrease, and the intervals
of concavity.
(b) Find the local extreme values and the inflection points.
(c) Sketch of graph.