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研究所、轉學考(插大)-微積分
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97年 - 97 國立暨南國際大學_轉學生入學考試試題_資工系二:微積分#124585
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題組內容
1. (20%)
(a) (10%) Please give an ε and δ and show that
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(Hint: ||a|-|b||＜|a-b|)
其他申論題
(a) Find the value of k that makes this a probability density function. (5 分)
#529834
(b) Find
#529835
(c) Find the marginal density function for Y1 and Y2.
#529836
(d) Please find the expected value of Y1, E(Y1).
#529837
(b) (10%) Let g be a function defined at least on some open interval containing the number 0. We say that g is of smaller order than h, or that g(h) is little-o(h) and write g(h) = o(h), if and only if g(h) is small enough compared with h that = 0. Show that h3 = o(h).
#529839
2. (15%) Show that ln(1+x) ≈ x as x→0. (Hint: (ln(x))'=1/x)
#529840
(a) (10%) Find the critical numbers of F and determine theintervals on which F is increasing and the intervals onwhich F is decreasing.
#529841
(b) (10%) Determine the concavity of the graph of F and find thepoints of inflection (if any).
#529842
(a) (10%) Verify that the region below the graph of f(x) = 1/x, x≥1 has infinite area.
#529843
(b) (10%) Suppose that the region (a) is revolved about the x-axis, what is the volume of the resulting solid ?
#529844
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