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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
1.
(b) Sketch the graph of the first derivative ℎ' (x) where ℎ(x) = |x − 1| + |x + 2|. (5%)
其他申論題
(a)請求出函數之弧長(arc length)。(6 分)
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(b)請求出此函數繞 x 軸旋轉所得到之表面積。(6 分)
#496769
9. 有一極坐標函數為r = f (θ) =1-2sinθ 。請求出此函數內環(inner loop)所圍出來之面積。(7 分)
#496770
(a) Find an equation of the tangent line to the curve y = at the given point (1, −1). (5%)
#496771
(a) (5%)
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(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
(b) Evaluate the indefinite integral ∫ f(x)dx. (7%)
#496777
(a) Prove that the inequality holds for any function f(x) that is continuous on [a, b]. (5%)
#496778
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