課程名稱︰微積分乙上 課程性質︰系定必修 課程教師︰劉瓊如 開課學院： 開課系所︰醫學院各系、農化、公衛、生科系 考試日期（年月日）︰97/11/11 考試時限（分鐘）：110min 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 limits of the following functions: 2 √(X +1) -1 a. lim ─────── x→0 2 x tan2x b.lim ───── x→0 tan5x 2.Find the derivative of a. f(x)=tan(xsinx) x-1 b. f(x)= ──── x+1 2 c. f(x)= x │x│ d. f(x)= │cosx│ 1 3.Let f(x)= xsin(──) if x =\= 0 x 0 if x = 0 a. Find lim f(x) x→0 b. f在0時是否連續？ c. f在0時是否可微？ 4.Find an equation of the tangent line to the hyperbola 2 2 x y ── - ── = 1 4 9 at (4,3√3). 5.Estimate √99.9 by linear approximation. 6.Find the absolutely extrema of the function. 2/5 f(x)= 5x -2x on [-1,2]. 7.Find all relative extrema and points of inflection of the function 1 f(x)= ───── . 2 x +1 8.Show that 2 3 3x < x + 3x if x > 0. 9.Show that the equation 2x-1-sinx = 0 has exactly one real root. --

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