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研究所、轉學考(插大)-微積分
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100年 - 100 國立成功大學轉學生招生考試_全校:微積分#113205
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題組內容
3. Calculate the following integrals :(各7%)
a)
其他申論題
(b) (4 points) spherical coordinates with order of integration dpdφdθ.
#483608
a) , where [x] is the Gauss function,
#483609
b) lim.
#483610
2. Find the local extrema of f(x) =x2 Inx for x ＞0, discuss concavity and find the point of inflection. (12%)
#483611
b)
#483613
4. Find the area of the surface generated by revolving the curve 6xy= x4+ 3 from x= 1 tox= 3 about the x-axis. (12%)
#483614
5. Use , prove , and find the sum . (12%)
#483615
6. Find the average value of f(x,y) = xy over the quarter circle x2 +y2≤1 in the first quadrant. (12%)
#483616
7. Evaluate F(x,y) = dt for x＞ 0, y＞ 0. (12%)
#483617
8. Find the points on the curve 17x2 + 12xy+ 8y2 = 100 that are closest to and farthest away from the origin. (12%)
#483618
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