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CalculusFormulas2008 - A.P Calculus Formulas 2008-2009...

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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. x (graph) 3. ceiling function (def) Least integer that is greater than or equal to x. 4. x (graph) 5. a b 3 3 a b a ab b b gc h 2 2 6. 3 3 a b a b a ab b b gc h 2 2 Hanford High School Calculus Richland, Washington 1 of 11
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7. f x x ( ) 1 (graph) -3 -2 -1 0 1 2 3 -3 -2 -1 1 2 3 x 8. p42 Change of base rule for logs: log ln ln a x x a 9. p579 Circle formula: 2 2 2 x h y k r 10. p580 Parabola formula: 2 4 x h p y k 11. p583 Ellipse formula: x a y b c a b 2 2 2 2 2 2 1 12. p585 Hyperbola formula: x a y b c a b 2 2 2 2 2 2 1 13. p591 eccentricity: e c a 14. sin cos 2 2 x x 1 15. 1 2 tan x sec 2 x 16. 1 2 cot x csc 2 x 17. sin u v b g sin cos cos sin u v u v 18. cos u v b g cos cos sin sin u v u v 19. tan u v b g tan tan tan tan u v u v 1 Hanford High School Calculus Richland, Washington 2 of 11
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20. sin( ) 2 u 2sin cos u u 21. cos( ) 2 u cos sin 2 2 u u 22. tan( ) 2 u 2 1 2 tan tan u u 23. sin 2 u 1 2 2 cos u 24. cos 2 u 1 2 2 cos u 25. tan 2 u 1 2 1 2 cos cos u u 26. sin sin u v 1 2 cos cos u v u v b g b g 27. cos cos u v 1 2 cos cos u v u v b g b g 28. sin cos u v 1 2 sin sin u v u v b g b g 29. cos sin u v 1 2 sin sin u v u v b g b g 30. law of sines: a A b B c C sin sin sin 31. law of cosines: 2 2 2 2 cos c a b ab C 32. area of triangle using trig. 1 Area sin 2 ac B 33. p32 parameterization of ellipse: 2 2 2 2 1 becomes cos , sin x y x a t y b t a b 34. p60 lim sin x x x 0 1 Hanford High School Calculus Richland, Washington 3 of 11
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35. p71 lim sin x x x   0 36. p83 Intermediate Value Theorem If a function is continuous between a and b , then it takes on every value between f a ( ) and f b ( ) .
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