作者just260km (小星)
看板NTU-Exam
标题[试题] 97上 刘琼如 微积分乙上 期中考
时间Sun Nov 23 21:29:11 2008
课程名称︰微积分乙上
课程性质︰系定必修
课程教师︰刘琼如
开课学院：
开课系所︰医学院各系、农化、公卫、生科系
考试日期（年月日）︰97/11/11
考试时限（分钟）：110min
是否需发放奖励金：是
（如未明确表示，则不予发放）
试题 :
1.Find the limits of the following functions:
2
√(X +1) -1
a. lim ───────
x→0 2
x
tan2x
b.lim ─────
x→0 tan5x
2.Find the derivative of
a. f(x)=tan(xsinx)
x-1
b. f(x)= ────
x+1
2
c. f(x)= x │x│
d. f(x)= │cosx│
1
3.Let f(x)= xsin(──) if x =\= 0
x
0 if x = 0
a. Find lim f(x)
x→0
b. f在0时是否连续？
c. f在0时是否可微？
4.Find an equation of the tangent line to the hyperbola
2 2
x y
── - ── = 1
4 9
at (4,3√3).
5.Estimate √99.9 by linear approximation.
6.Find the absolutely extrema of the function.
2/5
f(x)= 5x -2x on [-1,2].
7.Find all relative extrema and points of inflection of the function
1
f(x)= ───── .
2
x +1
8.Show that
2 3
3x < x + 3x if x > 0.
9.Show that the equation 2x-1-sinx = 0 has exactly one real root.
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