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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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6. (10 分) Prove that ln(1+x) =
，-1<x ≤ 1.
其他申論題
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..)
#521160
3. (10 分) Find the equation of the tangent line to the graph given by 2x3 + 2y3 = 9xy at the point (1,2).
#521161
4. (10 分) Find the dimensions of the isosceles triangle of least area that circumscribes a circle of radius r.
#521162
5. (10 分)Find the interval of convergence of the series .
#521163
7. (10 分)Find the volume of the solid generated by revolving about the x-axis the region bounded by the curve y =, the x-axis, and the lines x = 0 and x = 2.
#521165
8. (10 分) Let u = x2y3exz, where x = s2 + t2, y = 2st and z = s ln t. Find = ?
#521166
1. Determine the slope of the graph of 3(x² + y² )² = 100xy at the point (3, 1). (10 分)
#521167
2. Evaluate dx. (10 分)
#521168
3. Differentiate f(x) = . (10 分)
#521169
4. Find the area of the region between the graphs of f(x) = 3x³ - x² - 10x and g(x) = -x² + 2x. (10 分)
#521170
，-1<x ≤ 1.
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，-1<x ≤ 1.