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研究所、轉學考(插大)-微積分
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96年 - 96 國立臺灣師範大學_學士班轉學生招生考試試題_地球科學系二年級：微積分#122365
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題組內容
1. (每小題 10 分, 共 30 分) Evaluate the following.
(b)
dx = ?
其他申論題
6. Evaluate dx. (15 分)
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7. Find the curvature of the parabola given by y = x -x² at x = 2, and sketch the circle of curvature at (2, 1). (15 分)
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8.** Let R be the region bounded by the square with vertices (0, 1), (1, 2), (2, 1), (1, 0). Evaluate the integral ((x + y)²sin²(x - y)) dA. (15 分)
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(a) = ?
#521157
(c) dx = ?
#521159
2. (10 分) Sketch the graph of the function f(x) =.(need to point out all critical points, inflection points, local minimum points, and local maximum points, e.t.c..)
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3. (10 分) Find the equation of the tangent line to the graph given by 2x3 + 2y3 = 9xy at the point (1,2).
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4. (10 分) Find the dimensions of the isosceles triangle of least area that circumscribes a circle of radius r.
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5. (10 分)Find the interval of convergence of the series .
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6. (10 分) Prove that ln(1+x) =，-1<x ≤ 1.
#521164
dx = ?
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dx = ?