課程名稱︰微積分甲上 課程性質︰共同必修 課程教師︰劉崑山 開課學院：生農學院、管理學院 開課系所︰生工　生機　地質　科管 考試日期（年月日）︰2010/11/22 考試時限（分鐘）：110分鐘(可以超時到寫完為止) 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : -1 y-1 (1)(2pt) ytan (x)+2y+xe =2 find the equation of the tangent line at (0,1) 2 sin x (2)(1pt) f(x)=tan(e ),f'(x)=? lnx (3)(1pt) f(x)=(secx) ,f'(x)=? 3/4 2 1/2 (x+1) (x +1) (4)(2pt) f(x)= ──────── ,f'(0)=? 5 (3x+2) 3/x (5)(1pt) lim x =? x→∞ x ∫ lntdt 1 (6)(2pt) lim ────── =? x→1 2 x -2x+1 n + 1 n + 2 n + 3 n + n (7)(3pt) lim (──── + ──── + ──── + ... + ────)=? n→∞ 2 2 2 2 2 2 2 2 n + 1 n + 2 n + 3 n + n 2 tan (lnx) (8)(2pt) ∫────── dx=? x 2 2 (9)(2pt) ∫sec xtan xdx=? 2/x 2 e (10)(2pt)∫ ────── dx=? 1 2 x 3 ______ (11)(1pt) Estimate √27.27 by the linear approximation. (12)(3pt) Show that ｜sina - sinb｜≦｜a - b｜for all a and b. Show that 3x-1-sinx = 0 has exactly one real root. (13)(3pt) A right circular cylinder is inscribed in a sphere of radius R. Find the largest possible volume of such a cylinder. 3 x (14)(8pt) Sketch the graph of f(x) = ──── 2 x + 3 A. The domain. B. The x- and y- intercepts. C. The symmetry. D. All possible asymptotes. E. The intervals of increase and decrease, and the maximum and minimum. D. The intervals of concavity, and the points of inflection. ---------------試題結束--------------- --

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