課程名稱︰微積分乙
課程性質︰大一必修
課程教師︰王藹農
開課學院：管院ˋ社科
開課系所︰經濟 國企 財金 ...
考試日期（年月日）︰Nov. 8 2007
考試時限（分鐘）：110 (兩節課)
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :(總分40)(一題4分)
1. lim 1-cosx
x→0 2x^2
2. Find two tangent lines to y=x^2 through (x,y)= (1,-3)
3. Lemniscate 3(x^2+y^2)^2 = 100(x^2-y^2) , (x,y)=(4,2) dy/dx = ?
4. A man 6 feet tall walks at a rate of 5 feet per second toward a light
that is 20 feet above the ground . When he is 10 feet from the of
the light , at what rate is the length of his shadow changing ?
5. y= x^2-3x-4/x-2 graph? maxima? minima? asymptotes?
6. f(x)=√3 sinx+cosx graph? maxima,minima,inflection points?
7. A man is in a boat 2 miles from the nearest point on the coast.He is to go
to a point Q , located 3 miles down the coast and 1 mile inland.He can row
at 2 mi/hr and walk at 4 mi/hr , find the least time T = ? hours
8. A rectangular page is to contain 24 square inches of print.The margins at
the top and bottom are 1.5" , and the margins on the left and right are 1".
Find the least area of paper.
9. lim √1+√2+√3+...+√n
n→∞ √n^3
2π
10. F(x)= ∫x^2 sinθ^2 dθ F'(x)= ?
Ans:
1. 1/4
2. y+3=6(x-1) ; y+3=2(x-1)
3. -2/11
4. -15/7
5. no max&min
6. max=2 min=-2
7. 忘了
8. 54
9. 2/3
10.-2xsinx^4
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.112.224.29