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研究所、轉學考(插大)-微積分
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104年 - 104 國立臺北大學學士班暨進修學士班轉學生招生考試試題_資訊工程學士、通訊工程學系：微積分#116800
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題組內容
3.(20%) Let f(x)= x
2
In(1+x).Compute f
(n)
(0), the n
th
derivative of f evaluated at x = 0,by the following steps.
(a) Find the power series for f(x).(10%)
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(a) with y as the variable of the integration, ie write. (5%)
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(b) with x as the variable of the integration, ie write (5%)
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2.(20%) The Cobb-Douglas Model for the production function is P=bLaK1-a , where b and a are positive constants and a ＜1. We want to maximize the production Pwith the constraint that mL+nK =q, where m, n and q are positive constants. Show that the maximum production occurs when
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(b) Use part (a) to derive f(10)(0).(10%)
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(a)
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(b)
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(c)
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(d)
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5. (20%)Please sketch the curve y = . (You must describe the domain, intercepts, symmetry, asymptotes, interval of increasing or decreasing, local maximum and minimum values, and concavity and points of inflection.)
#499111
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