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研究所、轉學考(插大)-微積分
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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
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題組內容
1. Evaluate the following integrals:
(4)
(8 points)
其他申論題
10. Evaluate the integral, cos(2nx) sin(x)dx, where n is an integer. (10 分)
#506411
(1) (7 points)
#506412
(2)(8 points)
#506413
(3) ∫cos(2θ)cos(3θ)dθ (7 points)
#506414
2. Evaluate or explain the limit does not exist. (10 points)
#506416
3. Find the interval of convergence for the series (10 points)
#506417
4. Find all local maxima, local minima, and saddle points of the function f(x,y)=x3+3xy+y3. (15 points)
#506418
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)
#506419
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)
#506420
7. Explain the fundamental theorem of calculus (two parts in this theorem), no proof is needed. (10 points)
#506421
(8 points)
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(8 points)