AP Calculus Formulas Matawan Regional High School Calculus BC only material has a box around it.

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1 AP Clcls Formls Mtw Regiol High School Clcls BC oly mteril hs bo ro it.. floor fctio (ef) Gretest iteger tht is less th or eql to.. (grph) 3. ceilig fctio (ef) Lest iteger tht is greter th or eql to. 4. (grph) b ( b)( b b ) 6. b ( b )( b b ) 3 3 Mtw Regiol High School - Clcls

2 7. f ( ) (grph) Chge of bse rle for logs: log l l h y k 9. Circle forml: 0. si cos. t sec. cot csc 3. si( v) si cosv cos si v 4. cos( v) coscosv si si v 5. t( v) t t v t t v 6. si( ) si cos 7. cos( ) cos si cos ( ) si ( ) 8. t( ) 9. si t t cos Mtw Regiol High School - Clcls

3 0. cos. t cos cos cos. si si v [cos( v) cos( v)] 3. cos cosv [cos( v) cos( v)] 4. si cosv [si( v) si( v)] 5. cossi v [si( v) si( v)] 6. lw of sies: 7. lw of cosies: b c si A si B si C c b b cos 8. re of trigle sig trig. Are bcsi( A) 9. prmeteriztio of ellipse: 30. lim si 0 y b becomes cos t, y bsi 3. Itermeite Vle Theorem If fctio is cotios betwee b, it tkes o ll vles betwee f ( ) & f ( b). f h f 3. efiitio of erivtive f ( ) lim ( ) ( ) h0 h 3 Mtw Regiol High School - Clcls

4 33. ( c) () 35. (c) c ( v) v 38. ( v ) v v v v 39. v v 40. si cos 4. cos si 4. t sec 43. cot csc 44. sec sec t 45. csc csccot 46. slope of prmetrize crve: y y t t 4 Mtw Regiol High School - Clcls

5 47. erivtive forml for iverses f f ( ) f 48. si cos t 5. - cot 5. sec csc 54. e e 55. l 56. l 57. Etreme Vle Theorem If f is cotios over close itervl, f hs m mi vle over tht itervl 58. Me Vle Theorem If f() is ifferetible fctio over [, b], (for erivtives) the t some poit betwee b: f ( b) f ( ) f ( c) b 59. lieriztio forml L( ) f ( ) f ( ) ( ) 5 Mtw Regiol High School - Clcls

6 60. k f k f 6. Me Vle Theorem If f is cotios o [, b], the t some b (for efiite itegrls) poit c i [, b], 6. First fmetl theorem: f ( t) t f ( ) f c f b 63. Trpezoil Rle: T y y y 64. c h 0... y y 65. c 66. si cos 67. cos si c c sec t c csc cot c 70. sec t sec c 7. csc cot csc c 7. l c 73. e e c 74. l 75. t l cos c c 6 Mtw Regiol High School - Clcls

7 76. cot l si c l sec t c 77. sec 78. csc l csc cot c 79. rcsi c 80. rct c 8. rcsec c 8. Itegrtio by prts: v v v 83. orer for choosig i LIPET logs, iverse trig., polyomil itegrtio by prts: epoetil, trig 84. epoetil chge: y y e kt hlf-life l k 86. cotios compo iterest: A( t) A e 87. logistics ifferetil eqtio: o rt P K P M P t M 88. logistics growth moel M P Ae kt 89. srfce re bot is (Crtesi): b y S y 7 Mtw Regiol High School - Clcls

8 90. legth of crve (Crtesi): b y L 9. lim l 0 9. lim 93. lim 94. lim lim e 96. lim! 97. k k 0 ( ) 98. k k ( )( ) k k prtil sm of geometric series: 0. Wht series? r ( ) ( r r ) geometric, coverges to if r r f ( ) f ( ) 0. Mclri Series: P( ) f ( ) f ( ) ! 3! Mtw Regiol High School - Clcls

9 03. Tylor Series P( ) f ( ) f '( )( ) ( ) f '''( ) 3! 3 ( ) f ''( )! 04. Mclri Series for 05. Mclri Series for Mclri Series for e 3 4 e...! 3! 4! 07. Mclri Series for si si... 3! 5! 7! 08. Mclri Series for cos 4 6 cos...! 4! 6! 09. Mclri Series for l( ) 3 4 l( ) Mclri Series for t. Lgrge form of remier. Remier Estimtio Theorem : t ( ) c! f R M R! 3. Error of geometric trcte so so tht is icle E( ) Error: trcte ltertig series E() st ter ot icle 9 Mtw Regiol High School - Clcls

10 5. Wht series? reciprocl of fctorils, coverges to e 0! 6. Wht series? b b telescopig series, coverges to b 7. Wht series? p series, coverges if p p 8. Wht series? hrmoic, iverges 9. Wht series? ltertig hrmoic, coverges 0. eriv. of prmetrize crve: y y t t y. legth of crve (prmetric): L t t t b y. srfce re (bot -is): S y( t) t t t 3. positio vector (str form): i j b r t f t g t h 4. spee from velocity vector: spee = v ( t) 5. irectio from velocity vector: irectio velocity v( t) spee v( t) 6. polr to Crtesi: r cos, y r si 7. trjectory eqtios: cos v t o o y yo o v t si 0 Mtw Regiol High School - Clcls

11 8. slope of polr grph: r si r cos slope t ( r, ) r cos r si 9. slope of polr grph t origi: slope = t 30. re isie polr crve: A r r 3. legth of crve (polr): L r r 3. srfce re (polr): S r si( ) r Mtw Regiol High School - Clcls

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