A.P. Calculus Formulas



A.P. Calculus Formulas 2008-2009

Hanford High School, Richland, Washington revised 8/25/08

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. p42 Change of base rule for logs: [pic]

9. p579 Circle formula: [pic]

10. p580 Parabola formula: [pic]

11. p583 Ellipse formula: [pic]

12. p585 Hyperbola formula: [pic]

13. p591 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. law of sines: [pic]

31. law of cosines: [pic]

32. area of triangle using trig. [pic]

33. p32 parameterization of ellipse: [pic]

34. p60 [pic] 1

35. p71 [pic] 0

36. p83 Intermediate Value Theorem If a function is continuous between [pic]and [pic], then it takes on every value between [pic]and [pic].

37. p99 definition of derivative [pic]

38. p116 [pic] 0

39. [pic] 1

40. p117 [pic] [pic]

41. [pic] [pic]

42. p117 [pic] [pic]

43. p119 [pic] [pic]

44. p120 [pic] [pic]

45. p142 [pic] [pic]

46. p142 [pic] [pic]

47. p145 [pic] [pic]

48. p145 [pic] [pic]

49. p145 [pic] [pic]

50. p145 [pic] [pic]

51. p151 slope of parametrized curve: [pic]

52. p165 derivative formula for inverses [pic]

53. p166 [pic] [pic]

54. [pic] [pic]

55. p167 [pic] [pic]

56. [pic] [pic]

57. p168 [pic] [pic]

58. [pic] [pic]

59. p169 [pic] [pic]

60. p169 [pic] [pic]

61. p169 [pic] [pic]

62. p172 [pic] [pic]

63. p174 [pic] [pic]

64. p173 [pic] [pic]

65. p188 Extreme Value Theorem If [pic]is continuous over a closed interval, then [pic]has a maximum and minimum value over that interval.

66. p196 Mean Value Theorem If [pic]is a differentiable function over[pic],

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

67. p233 linearization formula [pic]

68. p236 Newton’s Method [pic]

69. p285 [pic] [pic]

70. p285 [pic] [pic]

71. p288 Mean Value Theorem If [pic] is continuous on [pic], then at some

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

72. p294 First fundamental theorem: [pic]

73. p307 Trapezoidal Rule: [pic]

74. p309 Simpson’s Rule: [pic]

75. [pic] [pic]

76. p332 [pic] [pic] [pic]

77. p332 [pic] [pic]

78. p332 [pic] [pic]

79. p332 [pic] [pic]

80. p332 [pic] [pic]

81. p332 [pic] [pic]

82. p332 [pic] [pic]

83. p332 [pic] [pic]

84. p332 [pic] [pic]

85. p332 [pic] [pic]

86. [pic] [pic]

87. [pic] [pic]

88. [pic] [pic]

89. [pic] [pic]

90. [pic] [pic]

91. [pic] [pic]

92. [pic] [pic]

93. p341 Integration by parts (formula): [pic]

94. p341 order for choosing u in LIPET[pic]logs, inverse trig., polynomial,

integration by parts: exponential, trig.

95. p351 exponential change: [pic]

96. p353 half-life [pic]

97. continuous compound interest: [pic]

98. p365 logistics differential equation: [pic]

99. p367 logistics growth model [pic]

100. p409 surface area about x axis (Cartesian): [pic]

101. p413 length of curve (Cartesian): [pic]

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

FORMULAS BELOW HERE ARE BC ONLY:

103. p450 [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. p475 What series? [pic] geometric, converges to [pic]if [pic]

114. p487 Maclaurin Series: [pic]

115. p489 Taylor Series: [pic]

[pic]

116. p491 Maclaurin Series for [pic] [pic]

117. p491 Maclaurin Series for [pic] [pic]

118. p491 Maclaurin Series for [pic] [pic]

119. p491 Maclaurin Series for [pic] [pic]

120. p491 Maclaurin Series for [pic] [pic]

121. p491 Maclaurin Series for [pic] [pic]

122. p491 Maclaurin Series for[pic]: [pic]

123. p496 Lagrange form of remainder [pic]

124. Taylor’s Inequality [pic]

125. p498 What series? [pic] reciprocal of factorials, converges to [pic]

126. p510 What series? [pic] telescoping series, converges to [pic]

127. p514 What series? [pic] [pic]series, converges if [pic]

128. p514 What series? [pic] harmonic, diverges

129. p517 What series? [pic] alternating harmonic, converges

130. p532 2nd deriv. of parametrized curve: [pic]

131. p533 length of curve (parametric): [pic]

132. surface area (parametric): [pic]

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

134. p542 speed from velocity vector: speed = [pic]

135. p542 direction from velocity vector: [pic]

136. p551 polar to Cartesian: [pic]

137. trajectory equations:[pic] [pic]

138. p552 slope of polar graph: slope at [pic]

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

140. p553 area inside polar curve: [pic]

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

142. surface area (polar): [pic]

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