作者rod24574575 (天然呆)
看板NTU-Exam
标题[试题] 99上 薛克民 微积分甲上 第四次小考
时间Sat Nov 13 20:15:17 2010
课程名称︰微积分甲上
课程性质︰必修
课程教师︰薛克民
开课学院：电资学院、工学院、管理学院
开课系所︰电机系、资工系、材料系、资管系
考试日期（年月日）︰99/11/01
考试时限（分钟）：25分钟
是否需发放奖励金：是
（如未明确表示，则不予发放）
试题 :
˙每题十分
˙请详述计算过程，无计算过程的答案不予计分
1. Peter moves east from his home with velocity 10 km/min. There is a library
lies north of Peter's home with distance 8 km. Peter, the library and his
home form an angle θ. How fast is the angle θ changing when the distance
between Peter and his home is x ？
Library
▕╲
▕θ╲
8 km▕ ╲
▕ ╲
▕ x ╲
Home ￣￣￣￣￣ Peter
┐ ┐ ┐ ┐
2. Prove that: for all real numbers x and y,│cos(x) - cos(y)│≦│x - y│
┘ ┘ ┘ ┘
3. Find all local extreme o the function:
╭
│ x^4 + 4x^3 + 8x^2 + 8x + 5 if x ≦ 0
f(x) = ┤
│ 2x^3 - 9x^2 + 12x - 3 if x ＞ 0
╰
What is the absolute minimum of f in [-2,2] ？
dF
4. Suppose that: ── = 3 - F(x) and F(0) = 1
dx
(a) Find F(x)
(b) Use linear approximation to approximate the value F(0.01) and F(-0.01)
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