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95年 - 95 國立臺灣師範大學_學士班轉學生招生考試試題_機電工程學系二年級：微積分#122367
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1. Determine the slope of the graph of 3(x² + y² )² = 100xy at the point (3, 1). (10 分)
其他申論題
5. (10 分)Find the interval of convergence of the series .
#521163
6. (10 分) Prove that ln(1+x) =，-1<x ≤ 1.
#521164
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
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
5. Evaluate ∫e2x cos 3x dx. (10 分)
#521171
6. Evaluatedx. (15 分)
#521172
(a) ;
#521173
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