89年 - 089 學士後西醫：微積分#84972

科目：微積分 | 年份：89年 | 選擇題數：0 | 申論題數：22

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所屬科目：微積分

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申論題 (22)

(c) If f(1)＞0 and f(3)＜0，there exists a number c between 1 and 3 such that f(c)=0.

(e) The average value of the function f(x)=1+x² on the interval [-1, 2] is 2.

(i) If f has continuous first partial derivatives in a neighborhood of the point (a, b), then f can have all of its directional derivatives at (a, b).

(j) If fx and fy both exist and equal at (a, b), then f is continuous at (a, b).

(b) If [x] denotes the greatest integer function, find.

4. If f is a quadratic function such that f(0) =1 andis a rational function, find the value of f’(0). (10%)

5. Find all functions f such that f’ is continuous andfor all real x. (10%)

6. Find the maximum and minimum values of x – y + z if (x, y, z) lies on the sphere x² + y² + z² = 1.(10%)

7. Find the area of the bounded region enclosed by curves y = x³ – 1 and y = 3x² – 2x – 1. (10%)