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研究所、轉學考(插大)-微積分
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105年 - 105 國立臺灣師範大學_學士班二年級轉學生招生考試試題_地球科學系、物理學系：微積分#120314
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題組內容
1. (12 points) Find the limit if it exists
(a)
其他申論題
(a) (8 points)Find the Taylor series generated by f(x) = 1/x at a = 2, and
#512504
(b) (4 points)where does the series converge to 1/x?
#512505
7.(8 points)Find the value of ∂z/∂x at point (1, 1, 1) if the equation xy + z³x - 2yz = 0 defines z as a function of the two independent variables x and y and the partial derivative exists.
#512506
8.(12 points)Find the absolute maximum and minimum values of f(x, y) = 2 + 2x + 2y - x² - y² on the triangular plate in the first quadrant bounded by lines x = 0, y = 0, y = 9 - x.
#512507
(b)
#512509
2. (8 points) Find an equation of the tangent line to the graph of x sin 2y = y cos 2x at the point.
#512510
(a)
#512511
(b)
#512512
4. (8 points) Let . Find (f-1)'(0).
#512513
5. (12 points) Consider the function given by f(x) = Find the interval of convergence for f(x).
#512514
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