80年 - 80 中原大學轉學生招生考試(理、工、資電學院聯招)：微積分#125375

(1)

(2)

(3)

(4)

(1)

(2)

3. Let f(x,y)=
Show that fx(0,0) and fy(0,0) both exist but the limit of f(x,y) at (0,0)
does not exist.

(1)

(1)

(2)

6. Find the Maclaurin series for , -1＜x＜1.

(a) The area of the surface z=x²+y² below the plane z=1 is (A) .

(b) The curvature $\kappa$ of the ellipse 4x²+9y²=36 at the point (3,0) is (B) .

(c) The local maximum value of f(x,y)=sin x + sin y + sin(x+y), 0＜x＜2pi, 0＜y＜2pi is (C) .

(d) The point P on the sphere x²+y²+z2=4 is closest to the point (3,1,-1), P= (D) .

(e) The volume of the solid that lies under the paraboloid z=x²+y², above the xy-plane, and inside the cylinder x²+y²=4 is (E) .

(f) Evaluate the line integral , where C is the circle x²+y²=9 is equal to (F) .