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）︰2018/10/11
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) lim x^5((cos(1/x^3))-1)
x→-∞
(b) cos(1/√θ)
lim ——————
θ→4/π^2 θ-4/π^2
2. (20 points) It is known that the slope of the graph y=sin(πxy)
at the point (1/3,1/2) can be expressed as a/(12-b) for some
real numbers a, b ∈ R. Find a and b.
3. (20 points) Find the values of dy/dx and d^y/dx^2 of the curve
y^3-3y = x^2-3 at the point (1,-2).