104年 - 104 國立臺灣師範大學_轉學生招生考試試題_數學系二年級：微積分#118784

科目：研究所、轉學考(插大)-微積分 | 年份：104年 | 選擇題數：0 | 申論題數：10

試卷資訊

所屬科目：研究所、轉學考(插大)-微積分

選擇題 (0)

申論題 (10)

(1) (7 points)

(2)(8 points)

(3) ∫cos(2θ)cos(3θ)dθ (7 points)

(4) (8 points)

2. Evaluate or explain the limit does not exist. (10 points)

3. Find the interval of convergence for the series (10 points)

4. Find all local maxima, local minima, and saddle points of the function f(x,y)=x³+3xy+y³. (15 points)

5. Find the absolute maxima and absolute minima of the function g(x,y)=x²+xy+y²-6x on the rectangular plate O≤x≤5,-3≤y≤3. (15 points)

6. Let C be a curve which is the intersection of two surfaces x²+y²=8 and x +z = 3. Find the tangent line to the curve C at the point P(2,2,1) . (10 points)

7. Explain the fundamental theorem of calculus (two parts in this theorem), no proof is needed. (10 points)