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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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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.)
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(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
(a) (5%) ∫ dx
#521190
(b) (5%) ∫ dx
#521191
(a) (10%) For a certain real number a, the following integral converges. Determine a and evaluate the integral.
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(b) (10%) For what values of the constants b and cwill the following limit exist and be equal to 1? dx .
#521193
3. (15%) If dis an arbitrary real number, let Sn(d) =. Determine the following limit: .
#521194
4. (10%) Let f(x) be a polynomial of degree m. Show that ∫exf(x)dx = ex(f(x) - f'(x) + f"(x) - ... + (-1)mf(m)(x))
#521195
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