作者FAlin (FA/钢)
看板NTU-Exam
标题[试题] 99上 蔡雅如 微积分甲上 第一次小考
时间Mon Oct 18 20:04:52 2010
课程名称︰微积分甲上
课程性质︰必修
课程教师︰蔡雅如
开课学院：电资学院 工学院
开课系所︰电机系 材料工程系 资工系 资管系
考试日期（年月日）︰2010/10/11
考试时限（分钟）：45分钟
是否需发放奖励金：是
（如未明确表示，则不予发放）
试题 :
1.Calculate the following limits.
(a) lim {√(x^2+ax)- √(x^2+bx)}, where a,b are constants.
x→-∞
1
sinx‧cos--- x>0
(b) lim f(x),where f(x)= x
x→0
x
--- x<0
[x]
([x] is the greatest integer funtion)
x^2, if x is irrational
2.f(x)=
0 , if x is rational
(a) At which number is f continuous?
,
(b) At which number is f differentiable? What is f(x)?
3.Difine functions of a∈R , f(a) and g(a), by the equations:
-1 e^x-1 -1 e^x-1
f(a)=lim tan (-------) and g(a)=lim _ tan (-------)
x→0 │x│^a x→0 │x│^a
(a) Find the domains of f(a)and g(a).
(i.e for what values of a do the above limits exist ?)
(b) Compute g(a) for all a in its domains, At which number is g discontinuous?
e^x-1
(Hint: lim (-------)=1)
x→0 x
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