※ [本文转录自 NTU-Exam 看板 #1AdpwufY ] 作者: iwantowaylaw (我要成为太鼓达人) 看板: NTU-Exam 标题: [试题] 时间: Thu Sep 3 11:57:43 2009 课程名称︰ 暑修微积分甲下第二次期中考 课程性质︰ 课程教师︰ 周青松 开课学院： 开课系所︰ 考试日期（年月日）︰2009/9/3 考试时限（分钟）：2小时 是否需发放奖励金：是 （如未明确表示，则不予发放） ------------------------------- 题目中好像有些笔误 我先不改喔 大家应该知道~ ------------------------------- 试题 : Make sure to give sufficient reason in each problem or you will NOT get any credit for your answer. A. (a) Set a = a1i + a2j + a3k and b = b1i + b2j + b3k Show that a x b = (a2b3-a3b2)-i(a1b3-a3b1)j+(a1b2-a2b1)k 无言不知道要证啥 (b) Set a = a1i + a2j + a3k b = b1i + b2j + b3k c = c1i + c2j + c3k | a1 a2 a3 | Show that (a x b) ‧ c = | b1 b2 b3 | | c1 c2 c3 | p.668 Example 3 B. (a)Find f(t) given that f'(t) = 2costi-tsint^2+2tk and f(0)=i+3k 应该不难吧 我算 f(t) = 2sint + 1 i + 1/2 cost^2 -1/2 j + t^2 +3 k (b)Find f(t) given that f'(t) = ti-t(1+t^2)^(-1/2)+te^tk and f(0)=i+2j+3k 重复 C. (a) Show that if γ is a differentiable vector function of t ,then the function r = ║γ║ is differentiable at where it is not zero and dγ dr γ‧ ── = r ── dt dt p.703 (14.2.3) 证明在p.704上方 (b) Show that for each integer n and all γ≠0 we have ▽r^n = nr^(n-2)γ 未知 D. (xy)^2 Set g(x,y) = ─── if (x,y) ≠ (0,0) x^4+y^4 0 if (x,y) = (0,0) dg dg (a)Show that ─(0,0) and ─(0,0) both exist and evaluate their values dx dy (b)Show that lim g(x,y) doesn't exist (x,y)→(0,0) p.785 第29题 要练习过吧 E. (a) Find all function with gradient yzi + (xz+2yz)j + (xy+y^2)k 未知 (b) 2xy Set f(x,y) = ─── if (x,y) ≠ (0,0) x^2+y^2 0 if (x,y) = (0,0) Show that f is not differentiable at (0,0) 应该是从不同方向逼近原点的值不同 所以不连续 所以不能微分吧!? ------------------------------------------ 感觉这篇过多非习题题目...... ------------------------------------------ --

※ 发信站: 批踢踢实业坊(ptt.cc) ◆ From: 140.112.4.94 ※ sky2857:转录至看板 NTUBIME103HW 03/26 22:15 --

※ 发信站: 批踢踢实业坊(ptt.cc) ◆ From: 140.112.7.214 ※ 编辑: ss355227 来自: 140.112.7.214 (05/14 15:14)