Calculus Exercises Sheet b)Let x be a variable,choose the right answer of four (20): Name Student Number: Speciality Question II III IV V 1)the domain of sinx is Mark A(-m,+o)B0,2)C.(-元，）D.(-l,1) I.Selections 2)the region of sinx is A(-p,+∞)B.0,2xC.(-g,π）D.(-1,1 a)Tick the box if it follows a function (10): 3)the domain of e'is 口f=G口=r<0 2 if x=L, f(x)=sinx, -x,otherwise, 口f国-2，fx=-山 A(-,+o)B.[0,+)C.(0,+o)D.(,+) f(x)=y,where y satisfies=The graph off(x)is shown as: 4)the region of e'is A(-a,+o)B.[0,+o)C.(0,+o)D.(L,+o) ocaoam-e0 5)the domain of logx is A(-,+o)B.0,+)C.(0,+o)D.(L,+m) 6)the region of logx is A(-,+o)B.0,+o)C.(0,+o)D.(L,+) ）the domain of x2-3is_ □ln6-s+o,the part graph of()isshown as:一人 A(-m,+0)B.[3,0C.[B+o)D.[N5,+o) 8)the region of x'-3 is A(-,+o)B.0,+o)C.[-3,+o)D.【N5,+o) 9)the domain of x+2 is A(-,+B.0,2]C.[-2,+o)D.(-,-2] 口fx)=sinl口fx)=g2(x,where g(x)=tanx,in(-π/2，x/2y, 10)the region of x+2 is A(-n,+∞)B.[0,2】C.[-2,+m)D.(-,-2】 口fx)= sinde") ++4-2in0+贴 口f)=sine,in(t 11)the domain of e'+logx is ()=sin((),where)2.ifs A(-n,+o)B.0,+)C.0,+)D.0,) -2,ifx20 An)is denoted asthe number of the studentsof the class n. A(-,+o)B(0,+∞)C.(L+)D.[L,+o)
2008 -2009 学年第 一 学期《高等数学 D》试卷--1 Calculus Exercises Sheet Name__________ Student Number:______________Speciality______________ Question I II III IV V sum Mark I. Selections a) Tick the box if it follows a function (10): f x x ( ) sin ; = f x( ) 0; = , 0, ( ) , ; x if x f x x otherwise = − 2, 1, ( ) 2, 1; if x f x if x = = − = − 2 2 f x y y x y ( ) , where satisfies 1; = + = The graph of ( ) is shown as: f x 1/ ( ) , (0, ); x f x e x = + sin , 0, ( ) , 0; x if x f x x if x = x 1 2 3 4 f(x) 1 2 1 1 x 0 0 1 f(x) 1 2 3 | | ( ) , 0; x f x at x x = = In (- , ), the part graph of ( ) is shown a + f x s: In (- , ), the part graph of ( ) is shown as + f x : 0 20 40 60 80 100 1st season 2nd season 3rd season 4th season f x( ) sin1; = 2 f x g x g x x ( ) ( ), where ( ) tan , in ( / 2, / 2); = = − 2 sin( ) ( ) , in (0, ); 4 2 x e f x x x = + + + − 2 cos ( ) sin( ), in ( , ); x x e f x e + = − + 2, if 0, ( ) sin( ( )), where ( ) ; 2, if 0 x f x h x h x x = = − f(n) is denoted as the number of the students of the class n. b) Let x be a variable, choose the right answer of four (20): 1) the domain of sin x is _______ A ( , ) B.(0,2 ) C. ( , ) D. ( − + − − 1,1) 2) the region of sin x is _______ A ( , ) B.(0,2 ) C. ( , ) D. ( − + − − 1,1) 3) the domain of x e is _______ A ( , ) B. [0, ) C. (0, ) D. − + + + + (1, ) 4) the region of x e is _______ A ( , ) B. [0, ) C. (0, ) D. − + + + + (1, ) 5) the domain of log x is _______ A ( , ) B. [0, ) C. (0, ) D. − + + + + (1, ) 6) the region of log x is _______ A ( , ) B. [0, ) C. (0, ) D. − + + + + (1, ) 7) the domain of 2 x −3 is _______ A ( , ) B. [3,0] C. [3, ) D. − + + + [ 3, ) 8) the region of 2 x −3 is _______ A ( , ) B. [0, ) C. [ 3, ) D. − + + − + + [ 3, ) 9) the domain of x + 2 is _______ A ( , ) B. [0,2] C. [ 2, ) D. − + − + − − ( , 2] 10) the region of x + 2 is _______ A ( , ) B. [0,2] C. [ 2, ) D. − + − + − − ( , 2] 11) the domain of log x e x + is _______ A ( , ) B.(0, ) C. [0, ) D. [ − + + + 0,1) 12) the domain of 1 x x − is _______ A ( , ) B.(0, ) C. (1, ) D. [ − + + + + 1, )
200g-2009羊率常一半和《灯各秋学路饮0-2 13)the domain of sinxr-I is b)Calculate the following limitations (40): A(-m,+o)B(0,+o)C.(1,+o)D.l,+m) )= 甲清 l4④the domain of sin(logx)）is_ A(-,+o)B.(0+o)C.f0,+m)D.L,+可 3)lin tany= 把兴 (L if x>l, 15)the domain of log(g(x))is,where g(x)=0 if x=1, 9© 片 -l,fx<1. A(-,+o)B.(0,+o)C.1+o)D.[l,+) 刀细+= 9四行 9 lim(sinx+1)= 10)limlog( II.Fill the Blanks (10) 1)1fm=0,hen)=— 以。 1☒H= 2》fm=2,e7— 1 13)linge"= 141im(-x+2）= )1f+的因.L,吗（化+A-= p 16)me= 17)lim cosx= 18)lim4= 4)If lim /(x)g(x)=0 and limg()=1,then limf()= 9)1i四= 20》g.cos(co(x》= 四l,如--— c)If im/()=3.limg(x)=2,then (10): III.Calculation )mU)+2gx)= 2)m6r产x)-8x= a)Value of functions (10): 3)linf(x)g(x)= 1)f(x)=sinx,thenf(0)= 2)f(x)=2x-1;thenf(1)= 5)limeu)sin(g()) 3)f(x)=cosx+e';thenf(x/2)= 4)f(x)=x2-logx;thenf(I)= ))then/(a) 6)f(x)=xx+2;thenf(2)= 7)f(x)=ve+1:thenf(0)= 8)f(x)=log(x2);thenf(ve)= 9f=2,g2)=3,theng(f)= 10/⑩=2g2=3.hen0+82. f1)g(2)
2008 -2009 学年第 一 学期《高等数学 D》试卷--2 13)the domain of sin 1 x x − is _______ A ( , ) B.(0, ) C. (1, ) D. [ − + + + + 1, ) 14) the domain of sin log( ) ( x ) is _______ A. ( , ) B. (0, ) C. [0, ) D. − + + + + (1, ] 15) the domain of log(g(x)) is _______, where 1, 1, ( ) 0, 1, 1, 1. if x g x if x if x = = − A. ( , ) B. (0, ) C. (1, ) D. − + + + + [1, ) II. Fill the Blanks (10) 1) If 0 lim ( ) 0 x x f x → = , then 0 lim ( ) x x f x → + =______ 2) If 0 lim ( ) 2 x x f x → = , then 0 1 lim x x f x( ) → − = ______ 3) If 0 0 ( ) ( ) lim h f x h f x L → h + − = , then ( 0 ) 0 lim ( ) ( ) h f x h f x → + − = ______ 4) If 0 0 lim ( ) ( ) 0 and lim ( ) 1, x x x x f x g x g x → → = = then 0 lim ( ) x x f x → =______ 5) If 0 ( ) lim 1, x f x → x = , then 0 lim ( ) x f x → = ______ III. Calculation a) Value of functions (10): 1) f x x f ( ) sin ; then (0) = = 2) 2 f x x f ( ) 2 1; then (1) = − = 3) ( ) cos ; then ( / 2) x f x x e f = + = 4) 2 f x x x f ( ) log ; then (1) = − = 5) sin ( ) ; then ( ) 1 x f x f x = = + 6) f x x x f ( ) 2; then (2) = + = 7) ( ) 1; then (0) x f x e f = + = 8) 2 f x x f e ( ) log( ); then ( ) = = 9) f g f (1) 2, g(2) 3, then ( (1)) = = = 10) 2 (1) (2) (1) 2, g(2) 3, then (1) (2) f g f f g + = = = b) Calculate the following limitations (40): 1) 3 2 lim x x → = 2) 1 lim x 1 x x → + = + 3) 0 lim tan y y → − = 4) 2 1 lim x 2 1 x →− x + = − 5) 1 lim x x x e → e + = 6) 2 1 1 lim t 1 t →− t − = − 7) 0 lim 1 x x → + = 8) 1 lim cos x 2 x → = − = 9) ( ) 2 0 lim sin 1 x x → + = 10) 1 limlog( ) t x →− = 11) 0 lim x x x → + = 12) 1 lim x x e →− − = 13) cos 0 lim x x e → = 14) ( ) 2 lim 2 x x →+ − + = 15) 0 1 lim x x → − = 16） lim x x e − →+ = 17） lim cos x x →− = 18） lim 4 x→+ = 19） 2 lim x t → = 20） / 2 lim cos(cos( )) x x → = c) If 0 0 lim ( ) 3, lim ( ) 2 x x f x g x → → = = ,then (10): 1) ( ) 0 lim ( ) 2 ( ) x f x g x → + = 2) ( ) 2 0 lim 3 ( ) ( ) x f x g x → + − = 3) 0 lim ( ) ( ) x f x g x → = 4) 0 ( ) 1 lim ( ) x f x → g x + = 5) ( ) 0 lim sin( ( )) f x x e g x → =
