2008-200的学年常一学期《高等学D(语)》试试®（）一2 2.Fill in the blanks (10 marks) 1)The domain of the function (2x os and the region of this function is 2)The discontinuous point of 3)The inverse function ofy=√2r-i+5is」 4)Suppose f(x)is differentiable,then the value of f(x)at x=a is,and 6sone-e+hy.m密 the slope of the tangent line of f(x)at this point is 5)If f(x)=-f(-x),then f(0)=_ and for any constant a,the definite integrationx- 7)f(x)=In(cosx)+tanx,then 6)rf)=e,hen∫ah。 x 7)If F(x),f(x),g(x),h(x)are continuous in (-o,).g(x)sf(x)sh(x)with 8)fe(e-4e+5cos(e-))di= limg(x)=limh(x)=L,F(x)is decreasing.then lim F(f(x)= 3.Calculations(30 marks) COSx ” 9)(x-1+id 2) 3x+sinx+100 lim o.le'+7Inx-1 10)I()=2.then (erus 3) 1io1-n0-x)=2008-2009 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 ________________ and the region of this function is _________________. 2) The discontinuous point of sin 1 x x e − is _________________________. 3) The inverse function of y x = −+ 2 15 is ______________________________. 4) Suppose f x( ) is differentiable, then the value of f x( ) at x a = is______, and the slope of the tangent line of f x( ) at this point is____________________________. 5) If fx f x () ( ) =− − , then f (0) = _____________, and for any constant a, the definite integration ( ) a a f x dx ∫− =________________. 6) If ( ) x fx e = , then f x '(ln )dx x = ∫ ____________. 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 → = ____________. 3. Calculations (30 marks) 1) 2 cos lim | | x x π x −   →    = 2) 8 3 sin 100 lim 0.1 7 ln 1 x x x x →+∞ e x + + + − = 3) ( ) sin 0 lim 1 ln(1 ) x x x → + − − = 4) ( tan ) d x e x dx = 5) 2 0 1 1 x d x dx x =   −     + = 6) Suppose ln x xy e y = + , then dy dx = 7) fx x x ( ) ln(cos ) tan = + , then 2 2 d f dx 8) ( ) 3 2 4 5cos( ) tt t t e e e e dt −− − − + ∫ = 9) 0 2 1 x x x dx ( 1) 1 − − + ∫ 10) If f f (0) 0, (1) 2 = = , then ( ) 2 1 ( ) 0 2 '( ) f x f x e dx ∫ =