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  1. 1a)
  2. http://www.wolframalpha.com/input/?i=derivative+of+e%5E%282s%29+arctan%28s%2F3%29+%2B+sin%28sqrt%28s%29%29
  3. d/ds(e^(2 s) tan^(-1)(s/3)+sin(sqrt(s))) = (3 e^(2 s))/(s^2+9)+(cos(sqrt(s)))/(2 sqrt(s))+2 e^(2 s) tan^(-1)(s/3)
  4.  
  5. 1b)
  6. http://www.wolframalpha.com/input/?i=derivative+of+%28ln%28t%5E4%2B5%29%29%2F%282%5Et+%2B+1%29+%2B+e%5E2
  7. d/dt((log(t^4+5))/(2^t+1)+e^2) = ((4 (2^t+1) t^3)/(t^4+5)-2^t log(2) log(t^4+5))/(2^t+1)^2
  8.  
  9. 1c)
  10. http://www.wolframalpha.com/input/?i=derivative+of+%282%2Bcosx%29%5E%28x%5E2%29
  11. d/dx((2+cos(x))^(x^2)) = x (cos(x)+2)^(x^2) (2 log(cos(x)+2)-(x sin(x))/(cos(x)+2))
  12.  
  13. 2a)
  14. integral (sin(x)+1/x^(1/3)+3^(2 x+1)) dx = (3 (x^(2/3) log(3)+9^x))/(2 log(3))-cos(x)+constant
  15. http://www.wolframalpha.com/input/?i=int+%28sinx+%2B+1%2F%28x%5E%281%2F3%29%29+%2B+3%5E%282x%2B1%29+dx
  16.  
  17. 2b)
  18. integral x cos(2 x) dx = 1/4 (2 x sin(2 x)+cos(2 x))+constant =
  19. 1/2 x sin(2 x)+1/4 cos(2 x)+constant
  20. http://www.wolframalpha.com/input/?i=int+%28xcos%282x%29%29+dx
  21.  
  22. 2c)
  23. integral (sin(x))/sqrt(4-cos^2(x)) dx = -sin^(-1)((cos(x))/2)+constant
  24. http://www.wolframalpha.com/input/?i=int+%28sinx+%2F+%28sqrt%284-cos%5E2%28x%29%29%29%29+dx
  25.  
  26. 2d)
  27. http://www.wolframalpha.com/input/?i=int+%28cos%5E5%28x%29%29+dx+-+sin%28x%29+%2B+2sin%5E3%28x%29%2F3+%2B+sin%5E5%28x%29%2F5
  28. Alternate answer: sin(x) - 2(sin^3(x))/3 - (sin^5(x))/5
  29.  
  30. 6)
  31.  
  32. a)
  33. Increasing on the intervals (-infinity,0), (3/2,infinity)
  34. Decreasing on the interval (0,3/2)
  35. Concave up on the intervals (-infinity, 0), (0,9/4).
  36. Concave down on the interval (9/4,infinity)
  37.  
  38. Critical points:
  39. x = 3/2: local minimum
  40. http://www.wolframalpha.com/input/?i=d%2Fdx+%28x%5E2-4x%2B3%29%2F%28x%5E2%29++%3D+0
  41. x = 0: jump discontinuity
  42.  
  43. Points of inflection: 9/4
  44. http://www.wolframalpha.com/input/?i=d%5E2%2Fdx%5E2+%28x%5E2-4x%2B3%29%2F%28x%5E2%29++%3D+0
  45.  
  46. b)
  47. Vertical assymtote on the line x = 0
  48. Horrizontal assymtote on the line y = 1 as
  49. lim_(x->infinity) (x^2-4 x+3)/x^2 = 1
  50. http://www.wolframalpha.com/input/?i=limit++%28x%5E2-4x%2B3%29%2F%28x%5E2%29+as+x+tends+to+infintity
  51.  
  52. c) http://www.wolframalpha.com/input/?i=plot+%28x%5E2-4x%2B3%29%2F%28x%5E2%29
  53.  
  54. d) http://www.wolframalpha.com/input/?i=plot+%28x%5E2-4x%2B3%29%2F%28x%5E2%29+from+x+%3D+0.5+to+4
  55.  
  56. 7b) 1/3
  57. http://www.wolframalpha.com/input/?i=d%2Fdx%28+1%2F%282+%28-2+-+x+%2B+Sqrt%5B5+%2B+4+x+%2B+x%5E2%5D%29%5E%281%2F3%29%29+-+%28-2+-+x+%2B+Sqrt%5B5+%2B+4+x+%2B+x%5E2%5D%29%5E%281%2F3%29%2F2%29+where+x+%3D+-2
  58.  
  59. 11a)
  60. integral (sin(x) cos(x))/sqrt(1+sin^2(x)) dx = sqrt(sin^2(x)+1)+constant
  61. http://www.wolframalpha.com/input/?i=integral+%28sin+x+cos+x%29+%2F+%28sqrt%281%2Bsin%5E2+x%29%29+
  62.  
  63. 11b)
  64. integral (6 x+8)/(4 x^2+12 x+13) dx = 3/4 log(4 x^2+12 x+13)-1/4 tan^(-1)(x+3/2)+constant
  65. http://www.wolframalpha.com/input/?i=integral+%286x+%2B+8%29%2F%284x%5E2+%2B+12x+%2B+13%29+
  66.  
  67. 12a)
  68. Does not converge
  69. http://www.wolframalpha.com/input/?i=integral+lnx+%2F+x+from+x+%3D+1+to+infinity
  70.  
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