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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