课程名称︰微积分甲上
课程性质︰必修
课程教师︰颜文明
开课学院：理学院
开课系所︰数学系
考试日期（年月日）︰2016/06/30
考试时限（分钟）：50
试题 :
1. If f(x) = (x-1)(x^2+x+1)/((2^x)(x^4+1)^(1/2)), find f'(1). (15 pts)
2. Find an equation of the tangent line to the curve y = x^2+x^3+x^4
at the point P(1, 3). (15 pts)
3. Given ε> 0, find a positive number δ(ε) such that
|x-1| < δ(ε) => |(x-1)(x-2)/((x-3)(x-4))| < ε (15 pts)
4. Find two constants a and b such that d/dx [(e^x)(acosx+bsinx)] = (e^x)sinx
(15 pts)
5. Let f(x) = (x+1)/((x+2)(x+3)), find f^(100) (x) (15 pts)
6. (a) Find d/dx sin^-1(x/3)
(b) Find d/dx (1/3)(tan^-1(x/3))
(c) Find d/dx ln(x+(x^2+9)^(1/2))
(d) Find d/dx cosx/(1+sinx)
(e) Find d/dx (x+x^(1/2))^(1/2)
(25 pts)