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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.
(A). Find the interval on which y =x
3
- 3x
2
+ 2x + 1 is both decreasing and concave downward. Answer. __(1)__
其他申論題
9.=________
#474886
(1)試求 f(x),h(x)之間的關係
#474887
(2)試求之值.
#474888
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?
#474889
(B). Find =__(2)__ and=__ (3)__ at the point x = 1, y = 1 of the curve x3+2y-2y4 =0.
#474891
(C)Evaluate. -Answers:__ (4)__ .
#474892
(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
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