※ 引述《dreamenjoy (今天也很爽)》之銘言：
: n 2
: 1. Find the limit lim Σ [Sin (iπ/n)] π/n
: n→∞ i=1
~~~~~~~ ~~~~~~~~~~~~~ ~~~~~
取和 高度 x 寬度 = 面積
考慮sin^2(x)在0~pi的黎曼和(這要靠一點經驗啦...最好畫圖輔助)
pi
原式= S sin^2(x) dx = pi/2
0
S是積分符號
: 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?)
想辦法證它收斂後代 lim an+1 = lim an = L
n->inf n->inf
解得L=2
: 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?
(350-10n)(200+20n)
(單位價格)(個數)
假設200+20n=x
則n=(x-200)/20
=>p(x)= (450-x/2)*x
R(x)=(450-x/2)*x^2
接下來就簡單了,我相信你會寫
: 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
先說我兩小題我都不太清楚..
第一小題我完全不會(遮臉)
第二小題應該是這樣
z=f(x,y)=y^2-x^2
固定y=1,f(x,1)=1-x^2(只考慮x方向)
所以fx(1,1)=-2 (x方向的斜率)
同理fy(1,1)=2 (y方向的斜率)
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◆ From: 140.113.91.60
※ 編輯: luke2 來自: 140.113.91.60 (04/24 20:33)
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04/25 01:18, , 1F
04/25 01:18, 1F
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