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97年 - 97 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#122361
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題組內容
3. Evaluate each integral.
(a) (5 分)∫x
2
e
x3
dx
其他申論題
1. (10 分) Show that the following limit does not exist.
#521117
(a) (5 分) f(x) =cos x
#521118
(b) (5 分) f(x) = + 5sin x
#521119
(c) (5 分) f(x) =
#521120
(b) (10 分)dx
#521122
4. (10 分) g(x) =f(t)dt, where $f$ is a function whose graph is shown as Fig. 1. Calculate g(6) and g'(6).
#521123
5. (5 分) Use the Integral test to determine the convergence or divergence of the following series.
#521124
6. (5 分) Use the Ratio or Root Test to determine the convergence or divergence of the following series.
#521125
7. (10 分) Find the tangent line to the curve of intersection of the surfaces z = x2 + y2andx + y + z = 33 at a point (1, 2, 5).
#521126
8. (10 分) Find the maximum value of f(x, y) = 2x + 2xy + y subject to the constraint 2x + y = 100 by Lagrange multiplier.
#521127
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