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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
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11. If y = y(x) satisfies the differential equation x
2
y' + 3xy = 2ln(x) for x ＞ 0 with y(1) = 2, then y(x)= __(13)__.
其他申論題
7. Let f(x)= sin(y+xcosy) dy. It follows that f'(0) = __(7)__.
#474849
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)__.
#474850
9.d= __(10)__.
#474851
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)__.
#474852
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)__.
#474854
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)__.
#474855
(a) =__ (18)__.
#474856
(b) If S1is the boundary surface of E (including all faces) endowed with the outward orientation, one has curl Fㆍ dS = __(19)__
#474857
(c) If S2 is the surface obtained from S1by removing the face in the xy-plane while keeping the orientation from S1 on all other faces, one then has curlF. dS =__ (20)__.
#474858
1.一賽車在圓形車道x2+y2=2500m2奔馳,而教練站在(25m,0)處。(m指公尺)當車在點(40m,30m)出，教練以雷達測知車子和他的距離以m/sec之比率增加,則此時車速為________ (以m/sec為單位)
#474859
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