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研究所、轉學考(插大)-微積分
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108年 - 108 國立臺北大學_日間學士班轉學生招生考試試題_通訊工程學系、資訊工程學系日間學士班二年級：微積分#118652
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題組內容
4. (15%) Evaluate the integrals:
(b)
其他申論題
1.(15%) Find the local maximum and minimum values and saddle points of the function f(x,y)=ey(y2-x2).
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2. (10%) The length width w, and height h of a box change with time. At a certain instant the dimensions are = 1m and w= h= 2 m, and and ware increasing at a rate of 2 m/s while h is decreasing at a rate of 3 m/s. At that instant find the rates at which the length of a diagonal are changing. (The length of diagonal L =)
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3.(25%) Sketch the graphs of (You need to describe A: domain; B: intercepts; C: asymptotes(horizontal and vertical if any); D: intervals of increase and decrease; E: local maximum and minimum values; F: interval of concavity; G: point of inflection; H: sketch the curve)
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(a)
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(c)
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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.
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(a)∫x2exdx(10%)
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(b) ∫xex^2dx (10%)
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(c) (15%)
#506173
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