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103年 - 103 國立臺灣師範大學_學士班轉學生招生考試試題_數學系二年級：微積分#120330
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題組內容
3. Evaluate the following integrals:
(4)
(8 points)
其他申論題
2. Find the equation of the tangent line to the graph of the equation x sin y = y cos x at the point. (10 points)
#512591
(1) (7 points)
#512592
(2) (7 points)
#512593
(3) (8 points)
#512594
4. Find the area under the parametric curve x = a(t - sin t), y = a(1 - cos t), 0 ≤ t ≤ 2π, a ＞ 0. (10 points)
#512596
5. Find the extreme values of f(x, y, z) = x - y + z on the unit sphere x² + y² + z² = 1. (10 points)
#512597
6. Integrate f(x, y, z) =over the involute curve x = cos t + t sin t, y = sin t - t cos t, z = 0, 0 ≤ t ≤ . (15 points)
#512598
(1) Explain the Mean Value Theory of the continuous function (differential form). No proof is needed. (5 points)
#512599
(2) Use the Mean Value Theory to prove that. (10 points)
#512600
1. 曉韻老師發現班上幼兒對於學習區的選擇，有偏好集中於某一區的趨勢。針對於此， 應如何因應？ (10 分)
#512601
(8 points)
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(8 points)