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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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8. The region ℛ enclosed by the curves y = x and y = x
2
is rotated about the x-axis. Find the volume of the resulting solid. (10%)
其他申論題
(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%)
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7. Find the point on the parabola y2 = 2x that is closest to the point (1, 4). (10%)
#496781
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)
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(b). (5 分)
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2. Find the derivative of y = (x2+1)3 . (10 分)
#496787
3. Find , given y3+y2-5y-x2+4=0 . (10 分)
#496788
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