[試題] 99上王振男微積分乙上期中考

看板NTU-Exam作者liltwnboiz (TCL)時間15年前 (2010/11/09 19:33)推噓4(4推 0噓 2→)

留言6則, 4人參與討論串1/1

課程名稱︰微積分乙課程性質︰必修課程教師︰王振男開課學院：醫學院開課系所︰醫學系考試日期（年月日）︰2010/11/09 考試時限（分鐘）：120 是否需發放獎勵金：是（如未明確表示，則不予發放）試題 : 1. Find the following limits. (a) (x^2)cos(x) lim ─────── x→0 1-sec(x) (b) (x^2) ∫ te^(-t^2)dt (0) lim ───────── x→∞ e^(-x^4) 2. For these two functions y=e^(x^x) and y=x^(e^x), the value of y approaches infinity as x approaches infinity. Determine which function grows faster and justify your answer. 3. Graph y=e^x-2e^(-x)-3x. Find out all the extremal points, where the function is increasing or decreasing, the concavity of the function, and the point of inflection, etc. 4. The function f(x) is continuous on [a,b]. 1, 2, ..., n are postive integers and x1, x2, ...., xn are points on [a,b]. Show that there exists a point c on [a,b] such that f(x1)+f(x2)+...+f(xn) f(c)= ──────────── n 5. The function f(x) is a strictly increasing function on [a,b]. Suppose its inverse function f^(-1)(x) is continuous on [f(a),f(b)]. Now define xj=a+(j/n)(b-a), j=1, 2, ..., n. Using the result from the last problem, we know that there exists a number cn in [a,b] such that f(x1)+f(x2)+...+f(xn) f(cn)= ──────────── n Does the limit of cn as n approaches infinity exist? If yes, find the limit. 6. 2y=x+4, y=x, and y-axis together form a triangular area. Find the volume of rotation of the area under the circumstances below. (a) Use the disk(washer) method, rotaion about x-axis. (b) Use the shell method, rotation about y-axis. (c) Use the shell method, rotation about the line x=4. (d) Use the disk(washer) method, rotation about y=8. (因為是憑記憶，所以有些用詞不精確...歡迎補充) -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 140.112.7.59 ※ 編輯: liltwnboiz 來自: 140.112.7.59 (11/09 19:34) ※ liltwnboiz:轉錄至某隱形看板 11/09 19:51

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shokanshorin

11/09 20:40, , 1^F

11/09 20:40, 1^F

※ 編輯: liltwnboiz 來自: 140.112.7.59 (11/09 20:46)

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raymond123

11/09 20:54, , 2^F

11/09 20:54, 2^F

※ 編輯: liltwnboiz 來自: 140.112.7.59 (11/09 20:55)

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woieyufan