do #52

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!

39. lim (2x)* 47. lim (1+ x2) 1/x * + 00 40. lim (2/x)* 48. lim tan x cos x X -> TT / 2 41. lim (sinx)* Hint: use the Squeeze Theorem. 49. lim tan x sin(2x) x -+ 0+ X-> TT / 2 42. lim (1 - x) 1-x 50. lim 1 1 x- 1+ x-1+ Inx X - 1 43. lim (x) 1/x 5 51. lim X x -+0O x-+3+ X2 - 9 x - 3 44. lim (1/x)* 52. lim xtan(1/x) X - DO 45. lim (In x) 1-x 53. lim ( In x) 3 x-+1+ X 46. lim (1 + x) 1/ x 54. lim x+x - 2 x -+ 1 In x