課程名稱︰微積分甲上
課程性質︰工學院必修
課程教師︰王藹農
開課學院：理學院
開課系所︰數學系
考試日期（年月日）︰2018/12/28
考試時限（分鐘）：120
是否需發放獎勵金：是
試題 :
每題一分，共十分
t+1
1. f(x)=sin(e^x), ∫ f(x)dx = maximum, find t=?
t
2. 圖如 https://imgur.com/a/XRpSbga find O=f(x,y)=?
3. y = x / (1+kx), find orthogonal trajectoria.
1
4. ∫ [(1-x^7)^(1/3) + (1-x^3)^(1/7)]dx = ?
0
5. A tank contains 100L of water. A solution with a salt concentration of 0.4
kg/L is added at a rate of 5L/min. The solution is kept mixed and is drained
from the tank at a rate of 3L/min. After 20 minutes, salt y(t) = ?
6. 圖如 https://imgur.com/a/fnYXYHb , and r=1, find the area of the shaded
session.
7. r = 5 / (2-4cosθ) , sketch the graph
8. The ellipse x^2/a^2 + y^2/b^2 = 1, a>b is rotated about the x-axis. Find
the surface area.
9. ∫dx/(x^7-x) = ?
10. x = 3t/(1+t^3), y = 3t^2/(1+t^3) Find the area of the loop