98年 - 98 國立中興大學轉學考招生考試試題_機械、土木、電機、化工、材料二年級：微積分#110871

(a)

(b)

(c)

2. Evaiate.

3. Suppose f is continuous, f(0)=0, f(2) , f'(x)＞0,and.Find the value of the integral . (10%)

5. For what value of a is it true that.

6. Let f(x)=. Find the Maclaurin series for f and use it to find and . (15%)

(ii) Find the tangent to the cycloid at the point where t = π/3. (5%)

(iv) Find the length of this arch. (5%)

8. Find the local maximum and minimum values and the saddle points of function f(x,y) =.