104年 - 104 國立中山大學轉學生招生考試試題_材光系二年級：微積分#116021

(b) Find all relative extreme values of .(10%)

(a) Evaluate cos(nπx) dx. (10%)

(b) Evaluate dt.(10%)

(b) Determine the radius of convergence of the power series . (10%)

(b) Find the absolute maximum and minimum values of f(x,y) =2x²-4x+2y²-4y + 6 on the disk x²+ y²≤4. (10%)

(a) Let E = {(x,y)|0≤x≤1, 0≤y≤1,0≤x²+y²≤1).Evaluate the double integral ∫ ∫E xy dA. (10%)

(b) Find the work done by the force field F(x, y) = x²i - yj in moving (10%) a particle along the curve r(t)= (t,t²), O≤ t≤2.