作者arbuztw (Robguns)
看板NTU-Exam
標題[試題] 102下 林楨芸 微積分甲下 第三次小考
時間Thu Jun 26 14:40:56 2014
課程名稱︰微積分甲下
課程性質︰必修
課程教師︰林楨芸
開課學院：理學院
開課系所︰數學系
考試日期（年月日）︰
考試時限（分鐘）：50
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
QUIZ-3-11.10-14.3
1. Find the Taylor series of f(x) = (x-1)ln(1+3x) about x = 1. (10 points)
2 2t
2. Reparametrize the curve r(t) = 〈------- - 1, -------〉with respect to arc
t^2+1 t^2+1
length measured from the point where (1, 0) in the direction of increasing
t. (10 points)
3. Let C be the curve of intersection of the parabolic cylinder x^2 = 2y and
the surface 3z = xy. Find the exact length of C from the origin to the
point (6, 18, 36). (10 points)
4. Let
x^3y-xy^3
----------- if (x, y) ≠ (0, 0)
x^2+y^2
f(x, y) = ｛
0 if (x, y) ＝ (0, 0)
(a) Compute f_x(0, 0) and f_y(0, 0).
(b) Calculate f_x(x, y) and f_y(x, y) for (x, y) ≠ (0, 0).
(c) Determine whether f_x and f_y are continuous at (0, 0). (20 points)
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