TO: Next Year’s Calculus Students Attached is a summer homework packet, which will be DUE the first Friday of Calculus class in August. The material in the packet should be material you learned in Algebra II and Pre-Calculus. My recommendation is that you look over the problems in the packet when you receive it but that you wait until the week before school starts to work the problems so that you will remember the material very well when school starts. I am looking forward to seeing you in Calculus in August! CALCULUS SUMMER HOMEWORK This homework packet is due the first FRIDAY of school. It will be turned in the first Friday of Calculus class and will count as a daily grade. Work these problems on notebook paper. All work must be shown. Use your graphing calculator only on problems 44 - 55. Find the x- and y-intercepts and the domain and range, and sketch the graph. No calculator. 1. y  3. y  2. y  9  x 2 x 1 4. y  sin x,  2  x  2 7. y  cot x,  2  x  2 10. y  e x x x 6. y  tan x,  2  x  2 9. y  csc x,  2  x  2 5. y  cos x,  2  x  2 8. y  sec x,  2  x  2 11. y  ln x   1, if x  1  x 2  1, if x  0  12. y  3 x  2, if x  1 13. y   2 x  2, if x  0 7  2 x, if x  1  ______________________________________________________________________________ Find the asymptotes (horizontal, vertical, and slant), symmetry, and intercepts, and sketch the graph. No calculator. 14. y  1 x 1 15. y  1  x  2 16. y  2  2 x2  9  17. y  x2  4 x2  2x  4 x 1 _____________________________________________________________________________________ Solve. No calculator. 18. x  x  12  0 2 19.  x  2  x  1  x  5  0 2 3 20. 3x  2 x4 0 21.  2 x  5 x  1 3  x  2 2 0 _____________________________________________________________________________________ Evaluate. No calculator. 22. cos 25. sin 28. sec 5 6 7 4 4 3 23. sin 3 2 26. cos  29. csc  4 24. tan 27. tan 30. cot 5 4 2 3 2 3 Evaluate. No calculator.     31. tan  Cos 1    33. cos Sin  1 3      32. sec  Arc sin    2    2x    2   2   34. sec  Arc tan  4x   Solve. Give exact answers in radians, 0  x  2 . No calculator. 35. 2cos2 x  3cos x  2  0 36. 2sin 2 x  cos x  1 37. sin  2 x   cos x 38. 2 cos  2 x   1  0 39. 2csc2 x  3csc x  2  0 40. tan 2 x  sec x  1 x 41. 2 cos    3  0 42. tan  2 x    3 43. 2sin  3x   3  0 3 _____________________________________________________________________________________ Solve. Show all steps. Use your calculator, and give decimal answers correct to three decimal places. 44. e2 x  3  37 50  11 47. 4  e2 x 45. e2 x  5e x  6  0 46. e x  12e x  1  0 58. log 4  x 2  3x   1 49. ln  5 x  1  3 50. log 2 ( x  3)  log 2 ( x  1)  log 2 12 52. log6  log 4  log 2 x    0 51. log8  x  5  log8  x  2   1 53. log3 (log 2 (log5 25))  x _____________________________________________________________________________________ 54. The number of students in a school infected with the flu t days after exposure is modeled by the 300 function P  t   . 1  e4  t (a) How many students were infected after three days? (b) When will 100 students be infected? kt 55. Exponential growth is modeled by the function n  n0e . A culture contains 500 bacteria when t = 0. After an hour, the number of bacteria is 1200. (a) How many bacteria are there after four hours? (b) After how many hours will there be 8000 bacteria? Use the figure to find the limit. No calculator. 56. lim f  x  57. lim f  x  58. lim f  x  59. lim f  x  x 3 x  x   x0 60. lim f  x  x  5 Evaluate. Show supporting work for each problem (algebraic steps or sketch). No calculator. 61. lim x  3 64. lim x  6 x2  x  6 62. lim x3  x  5 x 0 x6  25 63. lim x  2 x 1 1 x 0 x 65. lim x 2  3x  18 2 x3  8 66. lim x2 x  x 3x  5 x 2 4 x2  1 Evaluate. Show supporting work for each problem (algebraic steps or sketch). No calculator. 1 1 67. lim 68. lim 2 x 3 x  3 x 3  x  3 69. ( ) { (a) (b) (3) Use the definition of the derivative to find the derivative. No calculator. f   x   lim h0 70. f  x   x 2  8 x 72. f  x   3 x4 f  x  h  f  x h . (You must know this formula.) 71. f  x   x9 73. f  x   x3  2 x 2  x  4