MATH 203 Final, Spring 2005

Seemann eed American University of Beirut iA RHICAN UNIV] .Mathematics Department | LIBKARY oF FUIROT Spring Semester 2004-2005 sn en omneree meena Math 203Final Exam = Circle your section: Section 1:11:00F Section 2 : 12:00 F Section 3 : 2 :00F Section 4: 3:00 F Part One # of correct answers # of wrong answers Part Two Total « Answer-table for the multiple choice questions. Circle the correct answer: 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 ] 2 3 4 5 6 7 8 9 0 1 2 3 4 5 lar elo] oc] oro] GS (60%) Part I; Circle the correct answer on the table provided on page one (Multiple choices, with 2 points for each correct answer and -0.25 point penalty on each wrong answer) 1. The two solutions of the quadratic equation 2x7~6x =0 are: ~a) 3 and 0 b) 2 and 0 c) -3 and 0 d) -2 and 0 . The coordinates of the vertex of the parabola y=x? +8 x are: a) (-5, -16) b) (-4,-25) c) (-4, -16) c) (-00,-2) U (3,400) d)_ [2,+00) . Given the logarithmic equation log, n =m. The equivalent exponential equation is: ajn" =z b)z"™ =n. 10. log, 1+ log, 6—log, 3= a) log, 3 b) log, ; ax 4] 11. lim 5 x90 2x° —3x 1 -1 a)~ b) 0 c) 2 d) — )5 ) ) ) 3 12. lim,_, sro) x+2 1 ~-1 aj— b) 0 d) — 5 ) c) 9% ) 5 a)2 b) 1 c) 0 d) -1 . x-yF : oe 14. Consider the system then the unique solution is: L ~x+3ys- “4) (L-1) b) (2-1) ©) (-1) 4) (2,1) Vx? —3x 15. The domain of definition of (x)= —~—— _ is x41 4... a)x#-l, x¥l1 b) 35 x<3 c) xS0,x33 d)0<sx<3 2x-y=0 16. The system 4x+y=-6 has x+2y=5 a) no solution b) a unique solution c) infinitely many solutions d) exactly two solutions . . 2 17. The solution set of the equation : 3x + ; =0 is xo + a)-3 b) 3 c) -2 d)2 2 In(i+1) in(i+ 19. de = i=] a) 12 b)9 ce) 11 d) 5 20. Gi ro x+3 if x<l then tim f(x) . Given f(x) = he! m f(x)= 2x4+1 if x21 xl a)2 b) 4 c)3 d). 1 ‘2. If fe) =x? -1, then f(2at1)= a) 3a? (3at2) b) 3a(3a+2) c) 4a? (a+) d) 4a(at+1) x? +5xt+6 | x+2 22. Gases x a) (x-2) b) (x +2) c) (+1) d) (x-1) ee 24. The value of a truck is estimated by the function: V = f(t) = 45,000 — 3,000z where V equals the value stated in dollars and t equals the age of the truck expressed in years, then the value of the truck will be equal to zero after: a)15 years b)16 years c) 22 years d)12 years 26. A step of (3x3) Gaussian elimination method has produced the following array: 10 O10 , . , then the solution set is: tees a) {(x, .x5.%5)/x, =X, =X; =0} b) {(x, 25545 )/y =0,x, =-2x,,x,€ R} c) {(x,,x,,x,)/x, =0,x, = 25,2, € R} d) {(x,,x,,%,)/x, =0,x, =-2x,,x, € R} 7 27.Domain f = a)R b) (2,+00) c) (2,40) d) (3,+00) 28.Range f= a) (3,+00) b) (2,400) c) (-2,400) d)R 29.The equation of the asymptote is: 30. The profit function for a firm is: P (q) = -10q * +3600q-45000 Where q equals the number of units sold and P equals annual profit in dollars. If 150 units were sold then the profit expected is equal to: a) $ 207 000 b) $ 249 000 c) $ 239 000 d) $ 270 000 4 (40%)Part II (Answer each of the following questions in the space provided. Justify and show your work) 1 0 -7 |-20 1) Given] 0 -2 -12 | 18 |, complete the remaining steps of the Gaussian method 0 0 5 15 and determine the solution (x,,x,,*3)- (8%) x+2 if xs0 2) Sketch function = 3) Solve the following equations: a) x?Inx-9Inx=0 c) |2x+3|=x-4 4) For each of the following find the limit (if it exists): . x-3 a lim,.,, (2%) xt+1 Is f(x) continuous at x = 1? Justify your answer. 5) For each of the following functions determine the derivative of y = f(x) using the tules of differentiation. (Don’t simplify your answer): a) y=3x?-5