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首頁 > 研究所、轉學考(插大)-微積分 > 107年 - 107 國立臺灣大學轉學生招生考試試題_理工科聯招：微積分(B)#110857 >

8. Let f(x) = arctan .The graph of f has a horizontal asymptote represented by the equation (8) and the global minimum value of f is(9).

其他申論題

8.周長為24 的三角形,其中一旋轉,則旋轉體的體積最大為多少? 此時三邊長為多少?(15%)

9.設其中0≤t≤2π為一曲線，試求線積分

7. Let f(x)= sin(y+xcosy) dy. It follows that f'(0) = __(7)__.

10. The third term of the Maclaurin series (i:e. the 'Taylor series centred at x = 0) of arcsin(3x) is __(11)__ (note that the answer should be a monomial in a； the term of ,' is counted as the0-th term). The radius of convergence of the series is __(12)__.

11. If y = y(x) satisfies the differential equation x2y' + 3xy = 2ln(x) for x ＞ 0 with y(1) = 2, then y(x)= __(13)__.

12. Let C be a variable path in the ay-plane of arc-length 1 starting at the point (,1) and ending at the point (a,b). Suppose that G(a,b) := .dr, where f(x,y) := arctan , is a function in a and b. Then, G attains its maximum at a =__(14)__ and b =__ (15)__ and the maxinum value of G is __(16)__.

13. If a and b are positive constants and if max{p,a} denotes the maximum between the numbers p and g, the iterated integral dy dx= __(17)__.

(a) =__ (18)__.

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