[考古] 99中興轉考

[dreamenjoy (今天也很爽)]

1. Find the limit lim  Σ  [Sin (iπ/n)]   π/n
                 n→∞ i=1








8.Let a1 = 4 and an+1 = 1/2(an+4/an), for n >= 1. Find lim an if it exists.
                                                       n→∞

(這題我算答案是2 不知道對不對?)



9. A store has been selling 200 DVD burners a week at $350 each.
A market survey indicates that, for each $10 rebate offered to buyers,
the number of units sold will increase by 20 a week.


(1) Find the demand (or price) function and the revenue function.
[hint: the demand function p(x) stands for the price
per unit that the company can change if it sells x units.
 The revenue function is defined by R(x) = xp(x),
if the company sells x units.]

(2) How large a rebate should the store offer to maximize its revenue?



10.Suppose that a bug is located on the hyperbolic paraboloid z = y^2 -x^2
at the point (1,1,0) In what direction should it move for the steepest
climb and what is the slope as it starts out?

麻煩各位大大了 感恩~

--
※ 發信站: 批踢踢實業坊(ptt.cc) 
◆ From: 111.242.106.155
→ a016258:8. YA 不過你要先證明它存在~
→ dreamenjoy:OK 那我只有其他三題有問題了
→ a016258:1. Riemann sum ...前幾天好像才剛看到~
→ dreamenjoy:第1題解出來囉! 我剩第10題不了解
推 ToMoveJizz:試試看方向導數
→ dreamenjoy:我有想到用方向導數 但是不確定答案
→ dreamenjoy:因為也沒正解@@