A.P. Calculus Formulas. 1. floor function (def) Greatest integer that is less than or equal to x.
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1 A.P. Clls Formls. floor ftio (ef) Gretest iteger tht is less th or eql to.. (grph). eilig ftio (ef) Lest iteger tht is greter th or eql to. 4. (grph) g h g h Pge
2 7. f ( ) (grph) Chge of se rle for logs: log l l 9. Cirle forml: h y k r. Prol forml: h 4 p y k. Ellipse forml: y. Hyperol forml: y. eetriity: e 4. si os t se ot s 7. si v 8. os v 9. t vg g si os os si g os os si si Pge v v v v t t v t t v. si( ) si os
3 . os( ) os si. t( ). si 4. os 5. t 6. si si v 7. os osv 8. si osv 9. os si v. lw of sies:. lw of osies: t t os os os os os vg os vg os vg os vg si vg si vg si vg si vg si A si B si C osc. re of trigle sig trig. Are si B. prmeteritio of ellipse: 4. lim si 5. lim si y eomes os t, y si t Pge
4 6. Itermeite Vle Theorem If ftio is otios etwee, the it tkes o every vle etwee f ( ) f ( ). 7. efiitio of erivtive f ( ) f h f lim ( ) ( ) h h ( ) g g vg v ( v ) v v F HG I vk J v v v si os os si t se ot s se se t s s ot Pge 4
5 5. slope of prmetrie rve: y y t t 5. erivtive forml for iverses f f ( ) f 5. si 54. os 55. t ot se s 59. ot ( ) 6. se ( ) 6. s ( ) t F os H G I K J F si H G I K J e l e Pge 5
6 64. l 65. Etreme Vle Theorem If f is otios over lose itervl, the f hs mimm miimm vle over tht itervl. 66. Me Vle Theorem If f ( ) is ifferetile ftio over,, (for erivtives) the t some poit etwee : f ( ) f ( ) f ( ) 67. lieritio forml L( ) f ( ) f ( ) ( ) 68. Newto s Metho 69. k f k f g f f g 7. f ( ) g( ) f ( ) g( ) 7. Me Vle Theorem If f is otios o,, the t some (for efiite itegrls) poit i,, f f 7. First fmetl theorem: f ( t) t f ( ) 7. Trpeoil Rle: T 74. Simpso s Rle: S h y y y y y h y 4 y y y 4 y y g g Pge 6
7 77. si os 78. os si 79. se t 8. s ot 8. se t se 8. s ot s 8. l 84. e e 85. l 86. t l os 87. ot l si 88. se l se t 89. s l s ot rsi Pge 7 rt rse 9. Itegrtio y prts (forml): v v v
8 94. orer for hoosig i LIPET logs, iverse trig., polyomil, itegrtio y prts: epoetil, trig. 95. epoetil hge: y y e kt 96. hlf-life l k 97. otios ompo iterest: A( t) A e o rt 98. logistis ifferetil eqtio: P kp M P t 99. logistis growth moel P M Ae Mk t. srfe re ot is (Crtesi): y S y. legth of rve (Crtesi): L y FORMULAS BELOW HERE ARE BC ONLY:. lim l. lim 4. lim 5. lim F HG I K J 6. lim e h Pge 8
9 7. lim! 8. k k 9. k k. k k ( ) ( )( ) 6 F HG ( ) I K J. prtil sm of geometri series: S r r h. Wht series? r geometri, overges to if r r f ( ). Mlri Series: P( ) f ( ) f ( )! f ( )! f ( ) 4. Tylor Series: P ( ) f ( ) f ( )( )! f ( ) g! g 5. Mlri Series for 6. Mlri Series for 7. Mlri Series for e e 4!! 4! 8. Mlri Series for si si 5 7! 5! 7! 9. Mlri Series for os os 4 6! 4! 6! Pge 9
10 4. Mlri Series for l( ) l( ) Mlri Series for t : t ( ) 5 7. Lgrge form of remier. Tylor s Ieqlity f R! M R! 4. Wht series?! reiprol of ftorils, overges to e 5. Wht series? 6. Wht series? g telesopig series, overges to lim p p series, overges if p 7. Wht series? hrmoi, iverges 8. Wht series? g ltertig hrmoi, overges 9. eriv. of prmetrie rve: y y t t. legth of rve (prmetri): L t y t F H G I K J F H G I K J t F H G I K J F H G I K J y. srfe re (prmetri): S y t t t Pge
11 . positio vetor (str form): r t f t i g t j h t k. spee from veloity vetor: spee = vtg 4. iretio from veloity vetor: iretio = veloity vetor spee 5. polr to Crtesi: r os, y r si g v t v t 6. trjetory eqtios: v os t o o y yo vosi t gt 7. slope of polr grph: slope t ( r, ) r r si os r os r si 8. slope of polr grph t origi: slope = t 9. re isie polr rve: A r 4. legth of rve (polr): L r F ri HG K J 4. srfe re (polr): S r si r F ri HG K J Pge
A.P. Calculus Formulas Hanford High School, Richland, Washington revised 8/25/08
A.P. Clls Formls 008-009 Hfor High Shool, Rihl, Wshigto revise 8/5/08. floor ftio (ef) Gretest iteger tht is less th or eql to.. (grph) 3. eilig ftio (ef) Lest iteger tht is greter th or eql to. 4. (grph)
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