所屬科目：研究所、轉學考(插大)-微積分
(a) (5 Points)
(b)(5 Points)
2. (10 Points) Find the point on the curve y = that is closest to the point .
3. (10 Points) Find the length of the parametric curve x=3t2,y=2t3, 0 ≤ t ≤ 1
4. (10 Points) Determine whether the improper integral is convergent or divergent.
5. (10 Points) Find the radius of convergence of the power series and evaluate
6.(10 Points) Find the equation of the tangent plane and the normal line to the surface at (1,1,0).
7.(10 Points) Let f : be a function. Assume that all second partial derivatives of f exist and continuous and Deine g :
8. (10 Points) Evaluate the double integral , sin(x+y)dA where D is the regsion bounded by x+y= π, x+y = 0 and x -y =π and x-y=0.
9.(10 Poins) Evaluate the triple integral , where E is the solid region in bounded by the surface z = 1 and z = x2+y2.
10. (10 Points) Evallate the line interal along the curve C : r(t) = (t2+1)i+ (t2 - 1)j, 0 ≤ t ≤ 2. Hint you may find a potential function f of the vector field F(x,y) = find f so that F = ∇f.
阿摩線上測驗
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that is closest to the point 
.
be a function. Assume that all second partial derivatives of f exist and continuous and
, sin(x+y)dA where D is the regsion bounded by x+y= π, x+y = 0 and x -y =π and x-y=0.
, where E is the solid region in 
bounded by the surface z = 1 and z = x2+y2.
along the curve C : r(t) = (t2+1)i+ (t2 - 1)j, 0 ≤ t ≤ 2. Hint you may find a potential function f of the vector field F(x,y) =
find f so that F = ∇f.