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研究所、轉學考(插大)-微積分
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111年 - 111 國立高雄師範大學_轉學生招生考試試題_電機工程學系二年級：微積分#116291
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題組內容
4. Let
Decompose the function into
.
(b) Evaluate the indefinite integral ∫ f(x)dx. (7%)
其他申論題
(a) (5%)
#496773
(b) (5%)
#496774
3. Show the area enclosed by the ellipse = 1 in Fig. 1 is 6π. (10%)
#496775
(a) Find the values of A, B and C. (3%)
#496776
(a) Prove that the inequality holds for any function f(x) that is continuous on [a, b]. (5%)
#496778
(b) Show thatdx . (5%)
#496779
6. Evaluate . (10%)
#496780
7. Find the point on the parabola y2 = 2x that is closest to the point (1, 4). (10%)
#496781
8. The region ℛ enclosed by the curves y = x and y = x2is rotated about the x-axis. Find the volume of the resulting solid. (10%)
#496782
9. The curve y = , −1 ≤ x ≤ 1, is an arc of the circle x2 + y2 = 4. Find the area of the surface obtained by rotating this arc about the x-axis. (10%)
#496783
Decompose the function into
.
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Decompose the function into .