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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
8. Let
(b) (10 points) Show that f is not continuous at (0,0).
其他申論題
5. (12 points) Consider the function given by f(x) = Find the interval of convergence for f(x).
#512514
6. (12 points) Find all local maxima, local minima, and saddle points of the function f(x, y) = 2x3 + 3xy + 2y3.
#512515
7. (12 points) Evaluate the double integral dA where R is the square with vertices (0,1), (1,0), (2,1), (1,2).
#512516
(a) (6 points) Compute fx(0,0) and fy(0,0).
#512517
1. (10 分) Use Newton's method to find the x-coordinate of the point where the curve y = x² - 2x crosses the horizontal line y = 1. Specifically apply Newton's method with the starting value x0 = 1 to get the first approximation x₁ = ? and then the second approximation x₂ = ? and omit all the other approximations xₙ, n ＞ 2.
#512519
2. (10 分) Find the length of the parameterized curve x = , 0 ≤ t ≤ 3.
#512520
(a) (10 分) Finddx.
#512521
(b) (10 分) Solve the differential equation .
#512522
(c) (10 分) Solve the differential equation 2y' = eˣ/² + y.
#512523
(a) (6 分) Find the limit of the sequence {aₙ}, where aₙ = .
#512524
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