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A.P. Calculus BC Formulas 2005-2006Hanford High School, Richland, Washington revised 3/8/06
1. floor function (def) Greatest integer that is less than or equal to x.
2. (graph)
3. ceiling function (def) Least integer that is greater than or equal to x.
4. (graph)
5.
6.
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7. (graph)
8. p34 Change of base rule for logs:
9. Circle formula:
10. Parabola formula:
11. Ellipse formula:
12. Hyperbola formula:
13. eccentricity:
14. 1
15.
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18.
19.
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20.
21.
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28.
29.
30. p581 law of sines:
31. p581 law of cosines:
32. p581 area of triangle using trig.
33. p27 parameterization of ellipse:
34. p57 1
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35. p67 0
36. p79 Intermediate Value Theorem If a function is continuous between and , then it takes on every value between and
.
37. p95 definition of derivative
38. p112 0
39. 1
40. p113
41.
42. p114
43. p115
44. p117
45. p135
46. p136
47. p138
48. p138
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49. p138
50. p138
51. p144 slope of parametrized curve:
52. p157 derivative formula for inverses
53. p159
54.
55. p159
56.
57. p160
58.
59. p161
60. p161
61. p161
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62. p164
63. p166
64.
65. p178 Extreme Value Theorem If is continuous over a closed interval, then has a maximum and minimum value over
that interval.
66. p186 Mean Value Theorem If is a differentiable function over ,(for derivatives) then at some point between and :
67. p221 linearization formula
68. p223 Newton’s Method
69. p269
70. p269
71. p272 Mean Value Theorem If is continuous on , then at some
(for definite integrals) point in ,
72. p277 First fundamental theorem:
73. p290 Trapezoidal Rule:
74. p292 Simpson’s Rule:
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75.
76. p315
77. p317
78. p317
79. p317
80. p317
81. p317
82. p317
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91.
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93. p323 Integration by parts:
94. p323 order for choosing u in LIPET logs, inverse trig., polynomial,integration by parts: exponential, trig.
95. p330 exponential change:
96. p332 half-life
97. continuous compound interest:
98. p343 logistics differential equation:
99. p343 logistics growth model
100. p389 surface area about x axis (Cartesian):
101. p397 length of curve (Cartesian):
102. Mr. Kelly’s e-mail address: [email protected]
103. p417 0
104. 1
105. 1
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106. 0
107.
108. 0
109.
110.
111.
112. partial sum of geometric series:
113. p459 What series? geometric, converges to if
114. p473 Maclaurin Series:
115. p475 Taylor Series:
116. p477 Maclaurin Series for
117. p477 Maclaurin Series for
118. p477 Maclaurin Series for
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119. p477 Maclaurin Series for
120. p477 Maclaurin Series for
121. p477 Maclaurin Series for
122. p477 Maclaurin Series for :
123. p482 Lagrange form of remainder
124. p483 Remainder Estimation Theorem
125. p484 What series? reciprocal of factorials, converges to
126. p494 What series? telescoping series, converges to
127. p497 What series? series, converges if
128. p498 What series? harmonic, diverges
129. p500 What series? alternating harmonic, converges
130. p514 2nd deriv. of parametrized curve:
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131. p514 length of curve (parametric):
132. p517 surface area (parametric):
133. p532 position vector (standard form):
134. p533 speed from velocity vector: speed =
135. p533 direction from velocity vector:
136. p555 polar to Cartesian:
137. p543 trajectory equations:
138. p560 slope of polar graph: slope at
139. slope of polar graph at origin: slope =
140. p562 area inside polar curve:
141. p564 length of curve (polar):
142. p565 surface area (polar):
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