109年 - 109 台灣綜合大學系統學士班轉學生聯合招生試題：微積分A#96944

(a)

(b)

3. (10 pts) Let x＞0 and △ABC be a triangle whose side lengths are . Choose a point P on , and a point Q on , and a point R on so that
  

 Let f(x) be the area of △PQR . Find the critical point and the minimum of f(x).

4. (10 pts) Find the radius of the convergence of the power series

5.(10 pts) Evaluate the improper integral

6. (10 pts) Let g :(0,∞)- be a twice differentiable function. Assume that
g(I)=I, g'(I)=3,g"(I)=-4.
Define a real valued function h on 

8. (10 pts) Evaluate the double integral

9. (10 pts) Let C be the curve in defined by the parametric equation
x(t)=cos(t),y(t)=sin(t),z(t)=t
for 0 ≤ t ≤ a. Suppose that the arc length of C is . Evaluate the line integal    of the vector field F=

10. (10 pts) Find the flux of the vector field F on defined by

through the surface S = oriented with upward pointing normal vector field.
備註:i=(1,0,0),j=(0,1,0),k=(0,0,1)