96年 - 96 淡江大學轉學考統計學#55963

科目：轉學考-統計學 | 年份：96年 | 選擇題數：0 | 申論題數：14

試卷資訊

所屬科目：轉學考-統計學

選擇題 (0)

申論題 (14)

1. Find the following integrals or limits:(每小題 6 points) (a) \x4 In^dx.

(b) ]7-~y^__dx.

(c) -dx. o(x +1)

(d) [ [(3jc2 +6^2)dydx.

(e) lim ^ + x___I.

2. Find 字 or (每小題 6 points) if ax ay In r (a)y= e3T

(b)y= —

(c)y= fl/(l +x ＞ 0

(d) g(x，y)

3. Find the maximum and minimum values for the function f(x) = jc3 - 3 x2 -24x+5 for x on the interval [-3, 8]. (lOpoints)

4. Find the relative extreme values of f(x, y) -y" + x3 -4xy. (10 points)

5. Find the Taylor series for ^dt at x=0. (lOpoints).

6. A manufacturer of digital clocks determines that he can sell x clocks per week at price p where x and p are related by the equation jc2 +3xp+/?2 = 4400. This equation determines demand as a function of price, x=Q(p), near the point (p0,x0)=(40, 20). (a) If price is increasing at the rate of 50% per week how fast is demand changing when p=$40? (8points)

(b) Find — at the point (p0,xoM40, 20). (8points) dp