2008-200的学年第一学期《高等学D(英语》期*李试试®(卷)一2 2.Fill in the blanks (10 marks) 1)The domain of the function (2x 1ogx-1】 isx><0 and the 到去em-eam+ eof this function is_(←o,log迈)U0og3迈，+o) 2)The discontinuous point of 3)The inverse function of yx+5 is (x-5)+1 2 1 4)Suppose f(x)is differentiable,then the value of f(x)at x=a isf(a) 一y 6)Suppose y=ef+y,then dx x-I and the slope of the tangent line of f(x)at this point is f(a) 5)If f(x)=-f(-x),then f(0)=0,and for any constant a,the definite integration f(xydx=0 6)If 1()-'.then ffnx ds-khc 刀f)=h(eos+amx,hend。-1+2sng x 7)fF(x,fx,g(x,hx)are continuous in(-o,o）.g(x)≤f(x)≤hMx)with limg(x)=limh(x)=L,F(x)is decreasing,then lim F(f(x))-F(L) B)ecod5sinec 3.Calculations(30 marks) 0 COSX 9引re-Wik=-240 945 2) 曾0 10)If f()=0.f(1)=2..then (f)ercd=4-l 3)1im(1-ln(1-x)=12008-2009 学年第一学期《高等数学 D（英语）》期末考试试卷（A 卷）--2 2. Fill in the blanks (10 marks) 1) The domain of the function 3 2 log 1 x x     −   is __{ 1} { 0} x x > <  _____ and the region of this function is __ 3 3 ( ,log 2) (log 2, ) −∞  +∞ _______________. 2) The discontinuous point of sin 1 x x e − is __x=0______________________. 3) The inverse function of y x = −+ 2 15 is _____ 2 ( 5) 1 2 x − + ____________. 4) Suppose f x( ) is differentiable, then the value of f x( ) at x a = is__ f a( ) ____, and the slope of the tangent line of f x( ) at this point is_______ f a'( ) __________. 5) If fx f x () ( ) =− − , then f (0) = __0____, and for any constant a, the definite integration ( ) a a f x dx ∫− =___0_____. 6) If ( ) x fx e = , then f x '(ln )dx x = ∫ _|x|+C___________. 7) If Fx f x gx hx ( ), ( ), ( ), ( ) are continuous in ( ,) −∞ ∞ . gx f x hx () () () ≤ ≤ with lim ( ) lim ( ) xa xa gx hx L → → = = , F x( ) is decreasing, then lim ( ( )) x a Ffx → = ___F(L)______. 3. Calculations (30 marks) 1) 2 cos lim | | x x π x −   →    = 0 2) 8 3 sin 100 lim 0.1 7 ln 1 x x x x →+∞ e x + + + − =0 3) ( ) sin 0 lim 1 ln(1 ) x x x → + − − =1 4) ( tan ) d x e x dx = 2 1 (tan ) cos x e x x + 5) 2 0 1 1 x d x dx x =   −     + =1 6) Suppose ln x xy e y = + , then dy dx = 1 2 1 x e y x x y − − 7) fx x x ( ) ln(cos ) tan = + , then 2 223 1 2sin cos cos d f x dx x x − =− + 8) ( ) 3 2 1 4 2 3 4 5cos( ) 5sin 2 3 tt t t t t t e e e e dt e e e C −− − − − −+ =+ − + ∫ 9) 0 2 1 240 ( 1) 1 945 x x x dx − − + =− ∫ 10) If f f (0) 0, (1) 2, = = , then ( ) 2 1 ( ) 2 2 0 2 '( ) 4( 1) f x f x e dx e = − ∫