MATH 204 Final, Summer 2004

MATHEMATICS 204 FINAL EXAMINATION Summer 2064 Circle vour section number : 1 (10:00, Dr. Abu-Idhuzain) 2 (11:15, Dr. Abu-Khuzam) 3 (8:45 , Dr. Lyzzaik) PROBLEM GRADE PART IL Benak US TERSTR LibikaRY of BEIRUT —_ 4 é . PAKT I. Answer each of the following problems in the space provided for each problem ( Problem 1 to Problem 5). (40 points) i. One card is to be drawn at random from a deck of 52 cards. Find the probability of selecting an ace or a heart. { 4 points] 2. Let fx») =)" exe 3v+6x +10. Determine the location and nature of all critical points. [ § points] atnéts ecenrte om P 3. Let f(x, y) =S5x* Inytx*y +e" (a) Find f, [ 2 points] (b) Find J [ 2 points} { 3 points] ry 4.° Sketch and find the area of the region bounded by the parabola y= 4-2* and the line [ 8 points] Z Pans 1 S. evaluate the following integrals. (a) fare” ax | 4 points] [ 4 points] x? (nx) dx [ 5 points] PART YJ, Circle the correct answer for each problem of part I] ( Problem 6 to Problem 20) in the TABLE IN PAGE 1. [4 points for each correct answer, -1/2 point penalty for each wrong answer]. (60 points) (i Qa 0) 6. Let A| 0 1 OQ |. Then | (i 0 -1) (a) Ab SA (b) Av =A (c) A? =O (zero matrix) (d) Ais not invertible (e) none of the above [4 points} 7. The number of ways in which 3 persons can be chosen from i0 persons so that one is a chairman, the second is a vice chairman and the third is a secretary Is. (a) y0Cs (b) 10° (d) 3 (e) none of the above [4 pomts} none of the above £4 points: } [x(x —l) dx = G (a) = oy (6) ~ Nea © - Mo » () Ay (e) none of the above [ 4 points] TI (e) none of the above [ 4 points] 1i. A box contains 5 mathematics books and 4 history books. 3 books are to be selected at random from the box without replacement, What 1s the probabilty that the first book will be a mathematics book and the second and third are history books? i2. A far coin is ta be flipped four umes. The probability that exactly 3 heads will occur ss: (c} id) (ei none of the above ' 4 pomis] Then £"(1) is equal to 30 40 none of the above { 4 points] i4.ber f(x,y) =— 2x7 +x 42x43 7 — 54. Then the point (1.2,-4) is: (a) a relative mmmum point (b) avelanve maximum point (c) a saddle poimt (d) none of the above [ 4 points] 6 , + fred The estimated value of the definite imegrai te ~ S}dx usmg the trapezoidal rule with n=4 (subdividing into 4 equal subintervals) 1s: {a) 4 9 (b) 43) ic} 48 (di i 4 points} 16, The marginal cosi (in dollars) of producing a productis AZC = 8x + 800, where x is the number of products produced. It is known that the total cost equals $60,000 when 40 units are produced (ie C(40}=60000), Then the total cost function is Cla = 4x74 8000 Cini= 4a°7800x-47.600 §00x+86,000 Cade 4x7 §00x+2 1.600 none of the above 14 | Q -2 | Then the determinant of the matrix of cofactors A, is equal to: 0 0 j 4 5 ) ) 16 ) 64 ) none of the above (a ( (c (3 if € i 4 points] fa b cy | 18. If As| de ff. such that |Aj=3, then Basd 3b+e 3c+ J) is equal to: ; Lg h i) Sa Sb S| g KS / | 3 3h 37! tn Ge Ws n ih in none of the above 1 4 pomts] 19. Given a random variable X which is normally distributed , with mean u =130 and standard deviation oO =8. The probability P (128<X < 142) is: iS (a) (b} (c) (d) (e) os Boo OR ° ®o te ta fe2) 1O MTN ron tA ° i 4 points} © f(x) = In(a* +2x+1). Then £'(0) is equal 10 trone of the above