n 2
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
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