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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:
(a)
其他申論題
5. What is the start building block of cholesterol? What is the control enzyme for cholesterol biosynthesis? What is the major transporter of cholesterol in circulation system? How the cells manipulate the oversupply of cholesterol? (10%)
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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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(b)
#506167
(c)
#506168
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?
#506169
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
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