A.P. Calculus Formulas



A.P. Calculus BC Formulas 2005-2006

Hanford High School, Richland, Washington revised 3/8/06

1. floor function (def) Greatest integer that is less than or equal to x.

2. [pic] (graph)

3. ceiling function (def) Least integer that is greater than or equal to x.

4. [pic] (graph)

5. [pic] [pic]

6. [pic] [pic]

7. [pic] (graph)

[pic]

8. p34 Change of base rule for logs: [pic]

9. Circle formula: [pic]

10. Parabola formula: [pic]

11. Ellipse formula: [pic]

12. Hyperbola formula: [pic]

13. eccentricity: [pic]

14. [pic] 1

15. [pic] [pic]

16. [pic] [pic]

17. [pic] [pic]

18. [pic] [pic]

19. [pic] [pic]

20. [pic] [pic]

21. [pic] [pic]

22. [pic] [pic]

23. [pic] [pic]

24. [pic] [pic]

25. [pic] [pic]

26. [pic] [pic]

27. [pic] [pic]

28. [pic] [pic]

29. [pic] [pic]

30. p581 law of sines: [pic]

31. p581 law of cosines: [pic]

32. p581 area of triangle using trig. [pic]

33. p27 parameterization of ellipse: [pic]

34. p57 [pic] 1

35. p67 [pic] 0

36. p79 Intermediate Value Theorem If a function is continuous between [pic]and [pic], then it takes on every value between [pic]and [pic].

37. p95 definition of derivative [pic]

38. p112 [pic] 0

39. [pic] 1

40. p113 [pic] [pic]

41. [pic] [pic]

42. p114 [pic] [pic]

43. p115 [pic] [pic]

44. p117 [pic] [pic]

45. p135 [pic] [pic]

46. p136 [pic] [pic]

47. p138 [pic] [pic]

48. p138 [pic] [pic]

49. p138 [pic] [pic]

50. p138 [pic] [pic]

51. p144 slope of parametrized curve: [pic]

52. p157 derivative formula for inverses [pic]

53. p159 [pic] [pic]

54. [pic] [pic]

55. p159 [pic] [pic]

56. [pic] [pic]

57. p160 [pic] [pic]

58. [pic] [pic]

59. p161 [pic] [pic]

60. p161 [pic] [pic]

61. p161 [pic] [pic]

62. p164 [pic] [pic]

63. p166 [pic] [pic]

64. [pic] [pic]

65. p178 Extreme Value Theorem If [pic]is continuous over a closed interval, then [pic]has a maximum and minimum value over that interval.

66. p186 Mean Value Theorem If [pic]is a differentiable function over[pic],

(for derivatives) then at some point between [pic]and [pic]: [pic]

67. p221 linearization formula [pic]

68. p223 Newton’s Method [pic]

69. p269 [pic] [pic]

70. p269 [pic] [pic]

71. p272 Mean Value Theorem If [pic] is continuous on [pic], then at some

(for definite integrals) point [pic] in [pic], [pic]

72. p277 First fundamental theorem: [pic]

73. p290 Trapezoidal Rule: [pic]

74. p292 Simpson’s Rule: [pic]

75. [pic] [pic]

76. p315 [pic] [pic] [pic]

77. p317 [pic] [pic]

78. p317 [pic] [pic]

79. p317 [pic] [pic]

80. p317 [pic] [pic]

81. p317 [pic] [pic]

82. p317 [pic] [pic]

83. [pic] [pic]

84. [pic] [pic]

85. [pic] [pic]

86. [pic] [pic]

87. [pic] [pic]

88. [pic] [pic]

89. [pic] [pic]

90. [pic] [pic]

91. [pic] [pic]

92. [pic] [pic]

93. p323 Integration by parts: [pic]

94. p323 order for choosing u in LIPET[pic]logs, inverse trig., polynomial,

integration by parts: exponential, trig.

95. p330 exponential change: [pic]

96. p332 half-life [pic]

97. continuous compound interest: [pic]

98. p343 logistics differential equation: [pic]

99. p343 logistics growth model [pic]

100. p389 surface area about x axis (Cartesian): [pic]

101. p397 length of curve (Cartesian): [pic]

102. Mr. Kelly’s e-mail address: Greg_Kelly@rsd.edu

103. p417 [pic] 0

104. [pic] 1

105. [pic] 1

106. [pic] 0 [pic]

107. [pic] [pic]

108. [pic] 0

109. [pic] [pic]

110. [pic] [pic]

111. [pic] [pic]

112. partial sum of geometric series: [pic]

113. p459 What series? [pic] geometric, converges to [pic]if [pic]

114. p473 Maclaurin Series: [pic]

115. p475 Taylor Series: [pic]

[pic]

116. p477 Maclaurin Series for [pic] [pic]

117. p477 Maclaurin Series for [pic] [pic]

118. p477 Maclaurin Series for [pic] [pic]

119. p477 Maclaurin Series for [pic] [pic]

120. p477 Maclaurin Series for [pic] [pic]

121. p477 Maclaurin Series for [pic] [pic]

122. p477 Maclaurin Series for[pic]: [pic]

123. p482 Lagrange form of remainder [pic]

124. p483 Remainder Estimation Theorem [pic]

125. p484 What series? [pic] reciprocal of factorials, converges to [pic]

126. p494 What series? [pic] telescoping series, converges to [pic]

127. p497 What series? [pic] [pic]series, converges if [pic]

128. p498 What series? [pic] harmonic, diverges

129. p500 What series? [pic] alternating harmonic, converges

130. p514 2nd deriv. of parametrized curve: [pic]

131. p514 length of curve (parametric): [pic]

132. p517 surface area (parametric): [pic]

133. p532 position vector (standard form): [pic]

134. p533 speed from velocity vector: speed = [pic]

135. p533 direction from velocity vector: [pic]

136. p555 polar to Cartesian: [pic]

137. p543 trajectory equations:[pic] [pic]

138. p560 slope of polar graph: slope at [pic]

139. slope of polar graph at origin: slope = [pic]

140. p562 area inside polar curve: [pic]

141. p564 length of curve (polar): [pic]

142. p565 surface area (polar): [pic]

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