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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
5.
(b) Show that
dx . (5%)
其他申論題
3. Show the area enclosed by the ellipse = 1 in Fig. 1 is 6π. (10%)
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(a) Find the values of A, B and C. (3%)
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(b) Evaluate the indefinite integral ∫ f(x)dx. (7%)
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(a) Prove that the inequality holds for any function f(x) that is continuous on [a, b]. (5%)
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6. Evaluate . (10%)
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7. Find the point on the parabola y2 = 2x that is closest to the point (1, 4). (10%)
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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%)
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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
10. Find an equation of the plane that passes through the points P(1, 3, 2), Q(3, −1, 6), and R(5, 2, 0). (10%)
#496784
(a) ; (5 分)
#496785
dx . (5%)
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dx . (5%)