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研究所、轉學考(插大)-微積分
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95年 - 95 國立臺灣師範大學_轉學生招生考試試題_資訊工程學系二年級：微積分#122368
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題組內容
5. (10 pts)Find the values of p for which each integral converges:
(a)
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其他申論題
3. (12 pts)Find the solution to dy/dx = 2xy(y²+1) that satisfies y(0) = 1.
#521180
(a);
#521181
(b)
#521182
(c).
#521183
(b).
#521185
6. (12 pts)The usual way to evaluate the improper integral I = dx is first to calculate its square: I² = dxdy. Evaluate the integral and solve the resulting equation for I.
#521186
7. (10 pts)Find the values of ∂z/∂x and ∂z/∂y at point (x,y,z)=(1, 1, 1) and z³ - xy + yz + y³ - 2 = 0.
#521187
8. (10 pts)Find the tangent and normal to the curve x³ + y³ - 9xy = 0 at point (2, 4).
#521188
9. (12 pts)Find the horizontal tangents to the graph of the cardioid r=1-cosθ, 0 ≤ θ ≤ 2π. (That is, find the points at which horizontal lines tangent to the curve.)
#521189
(a) (5%) ∫ dx
#521190
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