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研究所、轉學考(插大)-微積分
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105年 - 105 國立臺灣大學轉學生招生考試試題:微積分(B)#110861
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題組內容
Correctly number each of your answers to indicate which question is answered.
(H)Find the first three nonzero terms of the Mclaurin series of tan(x). Answer: __(9)__.
其他申論題
(D)Find the volume of the solid generated by revolving the following region about the y-axis: {(x,y) :0 ≤x ≤π and 0 ≤y ≤sinx}. Answer: __(5)__ .
#474893
(E) Find the arc length of the curve y = from x= 0 to x = π/3.Answer: __(6)__ .
#474894
(F) Find the solution of the differential equation y'=(1+2x)(1+y2) with the initial condition y(0) = 1. Answer: __(7)__.
#474895
(G) Find the solution of the differential equation y' + ytan(x) = sec(x) with the initial condition y(0) = 2. Answer: __(8)__.
#474896
(I) Let u = u(r, y) be a function of t, y. Express in terms of polar coordinates r,θ together with Answer: __(10)__
#474898
(J) Find the directional derivative of f(x, y, 2) =xy z2 at the point (e,e, 1) in the direction u = Answer: __(11)__.
#474899
(K) Find the critical points of f(x, y) = x2 + y4 + 3xy2 - 5x which are saddle points. Answer:__(12)__.
#474900
(L) Find the minimum of x2+ y2 + z2 for (x,y, 2) on the intersection curve of the two surfaces y + 2z = 1 and 3x2 + y2 -z2 = 1. Answer:__ (13)__.
#474901
(M) Evaluate dydx. Answer: __(14)__ .
#474902
(N) Let R be the region in the first quadrant of the xy-plane bounded by xy = 1, xy = 2, y = 2 and y = 2x. Evaluatedxdy. Answer:____ (15)____.
#474903
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