课程名称︰微积分乙上 课程性质︰必修 课程教师︰李聪成 开课学院：管院 开课系所︰ 考试日期（年月日）︰2013年1月10日 考试时限（分钟）：160分钟 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : 1.Evaluate the definite integral. 3 ∫ ㄧx^2-4ㄧdx 0 2.Find the area of the region bounded by the curves y=1/x , y=1/x^2 , x=2 3.Evaluate the indefinite integral. ————— ∫√ 5+4x-x^2 dx 4.Evaluate the limit. x x sint lim ( —— ∫ ——— dt) x→3 x-3 3 t 5.Evaluate the limit n n n n lim ( ———— + ———— + ———— + ...+ ———— ) n→+∞ n^2+1^2 n^2+2^2 n^2+3+2 n^2+n^2 6.Use logarithmic differentiation to find the derivative of the function ＿＿＿ x^3/4 √x^2+1 y= ——————— where x>0 (3x+2)^5 7.Show that f is one-to-one on [0, +∞) and find a formula for the inverse function f^-1, where ＿＿ 1-√ x f(x)= ————— ＿＿ 1+√ x 8.Find the volume of the solid obtained by rotating about x=1 the region bounded by y=4x-x^2 and y=3 9.Prove that log 5 is an irrational number. 2 10.Evaluate the limit. 1 cosx-1+ —x^2 2 lim ——————— x→0 x^4 用书：Stewart Calculus, 7th edition 范围：Ch4-Ch6 --

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