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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
.
(a) Find the values of A, B and C. (3%)
其他申論題
(b) Sketch the graph of the first derivative ℎ' (x) where ℎ(x) = |x − 1| + |x + 2|. (5%)
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(a) (5%)
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(b) (5%)
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3. Show the area enclosed by the ellipse = 1 in Fig. 1 is 6π. (10%)
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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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(b) Show thatdx . (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%)
#496782
Decompose the function into
.
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Decompose the function into .