do 32 and 36

Note: For the L'Hopital's Rule problems, be sure to check whether L'Hopital's Rule applies before using it!!!! If you don't the graders will take off points!

Note: For the optimization problems, be sure that you find the interval your function is valid on. And be sure that you show that your answer is actually an absolute max/min. These are the two steps that students most often skip!

27. lim x + 4x + 4x x--2 x3 + 7x2 + 16x + 12 Problems In x 28. lim In Exercises 9 - 54, evaluate the given limit. x too X 9. lim x + x - 2 29. lim In (x2) x -+1 x - 1 * + 0O X 10. lim x +x - 6 In x) x-+2 x2 - 7x + 10 30. lim * + 0O X 11. lim sin x 31. lim x . Inx X- T X - TT x -+ 0+ 12. lim sin x - COS X 32. lim Vx . Inx X-> TT / 4 COs(2X) x -+0+ sin (5x) 33. lim xe1/x 13. lim x -+ 0+ x -+ 0 X 34. lim x3 - x2 x -+ 0o 14. lim - sin (2x) x -+0 x +2 35. lim Vx - Inx x -+ 0O 15. lim - sin (2x) x-+0 sin (3x) 36. lim xe* * - - 00 16. lim sin(ax) x-+0 sin(bx) 37. lim 1 -1/x x -+ 0+ x2 17. lim x2 38. lim (1 + x) 1/x x -+ 0+ 339