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研究所、轉學考(插大)-微積分
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105年 - 105 國立臺北大學_日間學士班暨進修學士班轉學生招生考試試題_資訊工程、通訊工程學系日間學士班二年級：微積分#118653
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題組內容
1. Please evaluate the integrals:
(c)
(15%)
其他申論題
5.(20%) Given the series ,(a) find the series' radius and interval of convergence. For what values of x does the series converge (b) absolutely,(c) conditionally?
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6. (15%) Sketch the region of integration, and evaluate the integral.∫∫R xydA where R is the region bounded by the lines y=x,y =2x,and x+ y=2.
#506170
(a)∫x2exdx(10%)
#506171
(b) ∫xex^2dx (10%)
#506172
(d) ∫∫Dx + 2y dA, where D is the region bounded by the parabolas y = 2x2 and y = 1 + x2.(15%)
#506174
2. Please sketch the curve (You must describe the domain, intercepts, symmetry, asymptotes, increasing or decreasing, local maximum and minimum values, and concavity and points of inflection.) (15%)
#506175
3. If f(x,y)= f(x,y) exists? Why?(10%)
#506176
4. A rectangular box without a lid is to be made from 12m 2 of cardboard. Please use the method of Lagrange multiplier to find the maximum volume of such a box.(10%)
#506177
5. Pind the radius of convergence and interval of convergence of the series .(15%)
#506178
(1)
#506179
(15%)
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