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首頁 > 研究所、轉學考(插大)-微積分 > 105年 - 105 國立臺灣大學轉學生招生考試試題:微積分(B)#110861 >

題組內容

Correctly number each of your answers to indicate which question is answered.

(C)Evaluate. -Answers: (4) .

其他申論題

(2)試求之值.

2.設曲面S:x2+y2+z2=10上點(x,y,z)的溫度為T(x,y,z)=2xy+4yz，試問最高溫度與最低溫度為何?發生在何處?

(A). Find the interval on which y =x3 - 3x2 + 2x + 1 is both decreasing and concave downward. Answer. __(1)__

(B). Find =__(2)__ and=__ (3)__ at the point x = 1, y = 1 of the curve x3+2y-2y4 =0.

(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)__ .

(E) Find the arc length of the curve y = from x= 0 to x = π/3.Answer: __(6)__ .

(F) Find the solution of the differential equation y'=(1+2x)(1+y2) with the initial condition y(0) = 1. Answer: __(7)__.

(G) Find the solution of the differential equation y' + ytan(x) = sec(x) with the initial condition y(0) = 2. Answer: __(8)__.

(H)Find the first three nonzero terms of the Mclaurin series of tan(x). Answer: __(9)__.

(I) Let u = u(r, y) be a function of t, y. Express in terms of polar coordinates r,θ together with Answer: __(10)__

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