A.P. Calculus Formulas - University of Houston
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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