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研究所、轉學考(插大)-微積分
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106年 - 106 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#120316
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題組內容
3.
(a) (10 分) Find
dx.
其他申論題
(a) (6 points) Compute fx(0,0) and fy(0,0).
#512517
(b) (10 points) Show that f is not continuous at (0,0).
#512518
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
(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
(b) (8 分) Find the radius and interval of convergence of the series .
#512525
(c) (6 分) Evaluate.
#512526
(a) (8 分) Find the value of at the point (1, 1, 1) if the equationxy + z³x - 2yz = 0defines z as a function of the two independent variables x and y and the partial derivative exists.
#512527
dx.
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dx.