[轉錄][考古題] 94上張秀瑜微積分乙期中

看板NTUIB99作者Thitta (胖胖 )時間17年前 (2006/11/11 20:03)推噓8(8推 0噓 5→)

留言13則, 5人參與討論串1/3 (看更多)

※ [本文轉錄自 NTU-Exam 看板] 作者: diep (隱藏人物) 看板: NTU-Exam 標題: [試題] 94上張秀瑜微積分乙期中時間: Sun Nov 13 16:11:17 2005 課程名稱︰微積分乙上課程性質︰共同必修課程教師︰張秀瑜開課系所︰管院、地理、經濟考試時間︰94/11/10 試題 : 1. ___ (a) Find lim√x+1 -2/(x-3). x→3 應該是1/4 (b) Prove that lim x^2cos(1/x^2) = 0. x→0 用夾擊定理，課本88頁 (c) Find all values of a such that f is continuous on R, where { x^2, if x > a; f(x) = { { x+1, if x≦ a. 2 作x =x+1﹝是這樣嗎？﹞ (d) Give a short explanation of why the following approximation is valid. ____ √4.02 ≒ 2 + 1/4(0.02) 這啥？ 2.Show that the function g(x)= x∣x∣has an inflection point at (0,0), but g"(0) does not exist. dy 3 _ 3.Find —. (a) y = 2csc (√x) (b) tan(x/y) = x+y dx chain rule 答案好長...不會打...= = 4.If y = f(u) and u = g(x), where f and g are third differentiable function, d^2y d^2y (du)2 dy d^2u d^3y — = — (－) + — — . Find a formula for — similar to dx^2 du^2 (dx) du dx^2 dx^3 the one given above. 這題是課本197頁的第65題，老師最近一次上課有講過，有背有保佑 5.Prove that if a > 0 and n is any positive integer, then the polynomial function 2n+1 p(x) = x + ax + b cannot have two real roots. ...... 6.Find an equation of the line through the point (3,5) that cuts the least area from the first quadrant. 有人會這題嗎... 7.Sketch the graph of y = x^3 －1/x^3 + 1 事實證明，真的會考畫圖題，詳情請見第四章 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 219.86.33.91 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 140.112.240.101

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Thitta

11/11 20:15, , 1^F

11/11 20:15, 1^F

※ 編輯: Thitta 來自: 140.112.240.101 (11/11 20:32) ※ 編輯: Thitta 來自: 140.112.240.101 (11/11 20:33)

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christless

11/11 20:38, , 2^F

11/11 20:38, 2^F

※ 編輯: Thitta 來自: 140.112.240.101 (11/11 21:36) ※ 編輯: Thitta 來自: 140.112.240.101 (11/11 22:19)

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littlecutie