MATH 203 Final, Fall 2001

AMERICAN UNIVERSITY OF BEIRUT =| ee Final Exam-Math 203 Feb.,2002 ee .| Reserved for Corrector Grade of Part I Prob.1 Prob.2 Prob.3 Prob.4 Prob.5 EXAM GRADE: Instructions: Cc D> 1.Answer each question in déetailin the space provided Tor if. You may lose total credit for giving only the final answer. 2.The colored booklet is for your scratch work. It will not be collected. 3.Write your name and |.D. and circle your section number. Distribution of Grades Part I 60 points Part IE 1. 2+4 . 8 6 . 10 : 10 2 3 4 5 TOTAL: 100 POINTS -PART (20 choice questions. 5points for each correct,and -0.5 points foreach wrong) 5x? -3 - x? Given the function: y= f(x) = . Answer the questions 1-------7. A. 6 B.2 C. 4 . The discontinuities of the function occur at x = A. +2 B. + 2ond#,|> c.42 4 4 . The value of x for which f'(x)=0 is: A B. -1 c.0 D. 2 E." . The y-intercept of the graph of the function is: A. (3/2,0) B. (0,-3) C.(0,-2) D. (0,3/4) E. . The average rate of change in the value of the function,in moving from x = 0 tox =3 is: A. 39/20 B.3/4 C.63/20 D,51/20 E. . The graph of f(x) has m horizontal and n vertical asymptotes.Then m and n respectively are: A.tand2 B.3and2 C.2 and 3 D. 1 and 4 E. 8.Solve for x: log,(2x—5)—log,(x-4) =3. A.11/2 B. 9/2 C. 6 D.7 E. a oe A. 15 B. 5 C. -5 D. -1/5 10. Solve: x? In(x+4)-16In(x +4) =0. A. x=5,+3 B. x=4,-3 C.x=+4 D. x=+4,-3 E. 11. The domain of definition of the function: f(x) =Vx+3In(4-x) is: A.x#4,x¥-3 B.-3<x54 C.-38x<4 D.x<-30rx>4 €E. 12. yh ~2nl = n=0 A. 16 B.8 C.2 D. 4 \ 13.The slope of the line parallelto 2x-3y-12=0, is A. 23 ~~ B.3/2 C. -2/3 D. -3/2 E. 14.1 f(x)=x?-3x and g(x)=Vx+1, then f(g(3))= A.2 Bv2 C2 D4 €£ (-2)(/-8) = A4 B-2 C2w2 D2 16. if 3% =9 then x= AVJ2 BV C4 #£»0D.3 92797 17. Simpl implify: 32g 907 A. 1/3 °B.6 C. 146 D. 3 Ix+y=5 » then y= 3x-2y=4 A. -4 B. 1 C.4 D. -1 E. aN If [2x - 7= -5x ; then x= “A. -7/8 B14 C. -1or-3/2 D. 2 or -7/3 E. 18. Given the system: 20. If M(2,-3) is the midpoint of the segment connecting the points A(-1,-2) and B(x,y), then, (x,y)= A. (3,5) B.(5,-4) €.(-3,4) «OD. (3,-4) E. WRITE YOUR ANSWER AS: A or B or C or D or E nexttothe question number. PART Il:Answer the following five questions in the space provided below the question. 1.(2+4=6 Points)The demand function for a product is : q=f(p)= 400-5p. Where q is the quantity and p is the price in dollars. a)Determine,in terms of p, the quadratic revenue function R=g(p). b)What price should be charged to maximize total revenue? 2.(8 Points)Solve in detail: 34+2x < 5-x < 10+x 3.(6 Points)The following are results of gaussian elimination method applied to three systems of linear equations. Interpret the meaning of each result,by giving the solution if any. 1 0 5{10 a) 0 1 -2|-3 00 0;8 1; x<-l 4,(40 Points)Consider the function: y = f(x)=4*°? vi<x<0 x3 O<x<2 33; x22 Answer the following short questions: a) im f(x) = b) lim f(x)= 0) lim f(x) = oom e)ls f continuous at x =-1? Justify. f) lim f(x) = g) lim f(x) = 222- x2" pis ¢ continuous at x = 2? Justify. 5.(10 Points)Consider the function: y=f(x)= 2(x+1)? 8 . a)Find the y-intercept . b)Find the x-intercepts if any. c)Find the vertex. d)Find the equation of the axis of symmetry. e)Sketch the graph.