MATH 101 Final, Fall 2001

OF BEIRUY Time: 2 Hours MATHEMATICS 101 January 31, 2002 FALL 2001-2002 Prof. H. Abu-Khuzam FINAL EXAMINATION Circle your section number below: #5 (1:00 Th). #6 (2:00 Th) #7 (3:00 Th) #8 (4:00 Th) PROBLEM GRADE OF BEIKU't PART II 8-19 AMERICAN UNIVERSIT+ LIBRary OF BEIRUy PART I. Solve each of the following problems ( Problems 1, 2, 3, 4, 5, 6, and 7) in the space provided for each problem. 1. Let y=f tvrt3dt . Find “ - ax [ 7 points] 2. Find the area of the region bounded by the curves x = yvand x = y+2. [7 points] 3x. if x<2 3. Let f(x) = | ax +h. if x>2 Find the values of a and b such that f is differentiable at x=2 . Explain. (7 points] 4. Find the sides of a rectangle with perimeter 100 cm whose urea is as large as possible. [ 7 points] 5. Find any asymptotes, any maxima or minima , and sketch the graph for f(x) xt? [ 10 points] 6. Find lim 2x7 sin Y) (Show your work) yo [ 6 points] 7. Find the volume of the solid generated by revolving the region bounded by the graphs of and y =X about the y-axis. {| you can use cylindrical shells er washer(Disk) yeu method J. [ 8 points] PART II. Circle the correct answer in each of the following questions (problem 8 to problem 19 ) [ 4 points for each correct answer, 0) for no answer. and —1/2 for each wrong answer] : \ l ——~ dx * ler 1° | . 12 - 1 0 . none of the above. { 4 points] 9. Ir xi-3xyty'=3. then \” at the point (2.1) is equal to: { -1 0 1/2 none of the above [4 points] 1 10. futvey de ‘ a7 108 _ 1716 3 ce. none of the above. { 4 points] . jx[(2x° +4) 1k. lim —————— __iisequal to: vo 5x a, 2/5 b. -4/5 c 0 d. - 2/5 e. does not exist. 12. Let (x) = x7-2x", then (using the second derivative test) : f(x) has a local maximum al x= -1. f(x) has a focal maximum at x=1. f(x) has a local minimum at x= 0. f(x) has a local maximum at x=0. none of the above (4 points]. (4 sec xde 0 vlan none of the above. [ 4 points] 14. If fis continuous onan interval [ab] and c € (a,b), then which one of the folowing statements is TRUE ? f ’¢e)=0, then » has a local maximum or a local minimum al x = Cc. f bas atocal minimumat x=c, then f° (co) =0 if (c)sO.and Ff (c) <0. then f has a local minimum at x = c. te f’ (ce) =O, then / basa point of inflection at x= e. none of the above. (4 points]. 15. If [ fndr=sin 2x . then f(x) = 2 cos 2x 2sin 2x >. -(1/2)cus 2x cos 2x e none of the above. [ 4 points] 16, The length of the curve 4V2 an y= for 4/3 none of the above. [ 4 points]. or fo) = Set". hen fim LOA is equal to: hoo h 4 190 500 does NOt exist. [ 4 points] 18. The equation x* +7x +1=0 has a. no solution in the interval |-2.2 b. exactly three solutions in the interval (-2,2] exactly wo solutions in the interval [-2,2] exactly one solution in the interval {-2,2] none of the above { 4 points]. 19, The value of the constant k that will make the function xetl2, ifvs2 Kxos , —kx', ifx>2 continuous, is none of the above, [ 4 points]