作者arbuztw (Robguns)
看板NTU-Exam
标题[试题] 102下 林桢芸 微积分甲下 第三次小考
时间Thu Jun 26 14:40:56 2014
课程名称︰微积分甲下
课程性质︰必修
课程教师︰林桢芸
开课学院：理学院
开课系所︰数学系
考试日期（年月日）︰
考试时限（分钟）：50
是否需发放奖励金：是
（如未明确表示，则不予发放）
试题 :
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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