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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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2. (10 分) Find the length of the parameterized curve x =
, 0 ≤ t ≤ 3.
其他申論題
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
(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
(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
(b) (8 分) Find the radius and interval of convergence of the series .
#512525
(c) (6 分) Evaluate.
#512526
, 0 ≤ t ≤ 3.
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, 0 ≤ t ≤ 3.