2008-2009学第一学期《高等学D(英语)》期季试试()-」 同济大学课程考核试卷(A卷) 6)If f(x)is an integrable function,then there exists ce(a,b),such that 2010一2011学年第一学期 A.f(c)=b-a B.f'(c)=b-a 命题教师签名： 审核教师签名： 课号：122008 课名：高等数学D(英语)考试考查：考试 C.limf(x)=b-a 后a恤6-a D. 此卷选为：期中考试（人、期终考试（√人重考（试卷 年级 专业 学号 姓名 任课教师」 7)If limf(x)-lim f(x)=0.lim/)but exists,thenA 题号 三四 五 总分 得分 人得0 B=得0证es (注意：本试卷共5大愿，3大张槽分100分.考时间为120分钟.要录可出卿题过程，百则不子计分) 1.Choose a right answer of four to the following questions(10 marks) C. D=得版e做 1)For the following concepts of a function,D_ is not relative to a limitation A.continuity B.derivative C.ntegration D.vaiable 2)If a,b are in the domain of a decreasing function f(x),anda<b,then B 8)If f(x)is a continuous on interval [a,b],then in [a,b].f(x)at least haveC A.a critical point. B.a stationary point. A.fa)≤fb)B.f(a≥fb)c.f(a)=fb)D.fa)≈fb) C.an absolute maximum point D.an inflection point. 3)If f(x)is a bounded function defined on [a.b],then f(x)must be c 9)If F(x)is an antiderivative of f(x),C is any constant,then B is correct A.continuous B.differentiable C.ntegrable D.icreasing A.F(x)=Cf f(xyix B.F(x)=[f(xyds 4)limf(x)exists,thenD C.F(x)=f(x)+C Aimf田=fa, B.lim f(x)=f(a') D.F()-lim-f() h c.limf(x)=-limf()d） D.none isA.B.C.. 10)a and b are in the domains of f(x)and g(x),then_Ais correct. A.lim(f(x)g(x))=lim f(x)limg(x) B.（f(x)g(x'=f(xg'x) 5)If f(x),g(x)are differentiable in [a,b],where f(x)g(x)<0,then c Cfx)gx)d=∫(x)dsg(x)ds.fx)gxd=∫fx)dgx)达 A.(f(b)-f(a))(g(b)-g(a))<0 B.f(x)g'(x)<0 C.∫f(xyx-Jg(xdx<0 D.fagx)达<0 2008-2009 学年第一学期《高等数学 D（英语）》期末考试试卷（A 卷）--1 同济大学课程考核试卷（A 卷） 2010—2011 学年第一学期 命题教师签名：梁进 审核教师签名： 课号：122008 课名：高等数学 D（英语） 考试考查：考试 此卷选为：期中考试( )、期终考试( √ )、重考( )试卷 年级 专业 学号 姓名 任课教师 题号 一 二 三 四 五 总分 得分 （注意：本试卷共 5 大题，3 大张，满分 100 分．考试时间为 120 分钟。要求写出解题过程，否则不予计分） 1. Choose a right answer of four to the following questions (10 marks) 1) For the following concepts of a function, __D___ is not relative to a limitation A. continuity B. derivative C. integration D. variable 2) If a b, are in the domain of a decreasing function f x( ) , and a b < , then _B__ A. fa fb () () ≤ B. fa fb () () ≥ C. fa fb () () = D. fa fb () () ≈ 3) If f x( ) is a bounded function defined on [a,b], then f x( ) must be _C__ A. continuous B. differentiable C. integrable D. increasing 4) lim ( ) x a f x → + exists, then __D_________ A. lim ( ) ( ) x a fx fa → = , B. lim ( ) ( ) x a fx fa + + → = C. lim ( ) lim ( ) x a x a fx fa → + → = D. none is A. B. C.. 5) If f x gx ( ), ( ) are differentiable in [a,b], where f x gx () () 0  < , then __C_____ A. ( f b f a gb ga () () () () 0 − −< )( ) B. f xgx '( ) '( ) 0  < C. f x dx g x dx () () 0 < ∫ ∫ D. () () 0 b b a a f x dx g x dx < ∫ ∫ 6) If f x( ) is an integrable function, then there exists c ab ∈(,), such that__ A. fc b a ( ) = − B. fc ba '( ) = − C. lim ( ) x c fx b a → = − D. 1 ( ) ( ) b a f x dx b a f c = − ∫ 7) If lim ( ) lim '( ) 0, lim ''( ) 0 xa xa x a fx f x f x → → → = = ≠ but exists, then __A______. A. ( ) lim 0, '( ) x a f x → f x = B. ( ) lim 0 '( ) x a f x → f x ≠ but exists, C. ( ) lim , '( ) x a f x → f x = ∞ D. ( ) lim '( ) x a f x → f x ≠ ∞ but does not exist. 8) If f x( ) is a continuous on interval [a,b], then in [a,b], f x( ) at least have_ A. a critical point. B. a stationary point. C. an absolute maximum point. D. an inflection point. C__ 9) If F x( ) is an antiderivative of f x( ) , C is any constant, then _B___ is correct. A. F x C f x dx () () = ∫ B. () () x C F x f x dx = ∫ C. Fx fx '( ) ( ) = +C D. ( ) () ( ) limh fx h fx F x →∞ h + − = 10) a and b are in the domains of f x gx ( ) and ( ) , then _A__ is correct. A. lim ( ) ( ) lim ( )lim ( ) ( ) x a xa xa f xgx f x gx → → → = B. ( f xgx f xg x ( ) ( ) ' '( ) '( ) ) = C. f x g x dx f x dx g x dx ()() () () = ∫ ∫∫ D. ()() () () b bb a aa f x g x dx f x dx g x dx = ∫ ∫∫