95年 - 95 台灣聯合大學系統(清、交、陽、中四校聯招)學士班轉學生聯合招生試題：微積分#113220

1. Let
If the function f is continuous on the entire real line. Then a =_________.

2. Let
 Then f_xy(0,0) = f(x, y) = and f_yx(0,0) =__________.

3. Let f(x) = .Then the interval of convergence of f(x) is________.

 and the interval OF convergence of f'(x) is________.

4. Let R be the region inside the ellipsoid  where a,b,c> 0, and abovethe plane z = b-y, then the volume of the region R is =______.

(a)

(b)

(a)

(b) dx.  Hint: for a ＞ 0,a ≠ 1.

(a)

(b)

9. Show that

10 Consider the funetion f(x,y) = ax² + βy². Find values for a and β so that (a) (0,0) is a local minimum (b) (0,0) is a local maximum, and (c) (0,0) is a saddle.