105年 - 105 國立暨南大學轉學生招生考試試題_微積分_(財金系、經濟系)#123387

科目：研究所、轉學考(插大)-微積分 | 年份：105年 | 選擇題數：0 | 申論題數：16

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所屬科目：研究所、轉學考(插大)-微積分

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申論題 (16)

(a) ∫(e2x + e-3x)dx =______.
(b) ∫dx =__________.
(c) ∫4x(2x² + 1) 7dx = _________.
(d) dx =________.
(e)dx =_________.
(a)=___________.
(b) limx→a[2 f(x) - 3g(x)] = ____________ , given that limx→af(x) = 3 and limx→a g(x) = 4.
(a) Suppose y = 2u² + 1 and u = x² + 1, find dy/dx =_________.
(b) Suppose y² - xy = 8, find dy/dx =___________.
(c)  Suppose y = x x+3, find dy/dx =____________.
4. Find an equation of the tangent line to the graph of y = e2x-3 at the  point (, 1). Ans:___________.
(a) Find absolute maximum value = ___________.
(b) Find absolute minimum value =___________.
6. Solve the equation 4et-1 = 4. Then t =___________.
1.The rectangular region R shown in the accompanying figure 
represents a city's financial district. The price of land in the district
is approximated by the function
p(x, y) = 200 - 10(x - )² - 15(y - 1)²
where p(x, y) is the price of land at the point (x, y) in
dollars/square foot and x and y are measured in miles. What is the
average price of land per square foot in the district? (15%)
2. The price-earnings ratio (PE ratio) of a stock is given by
R(x, y) =
where x denotes the price per share of the stock and y denotes the earnings
per share. Estimate the change in the PE ratio of a stock if its price
increases from $60/share to $62/share while its earnings decrease from
$4/share to $3.80/share. (15%)