CalculusFormulas2005 - A.P Calculus BC Formulas 2005-2006...

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A.P. Calculus BC Formulas 2005-2006 Hanford High School, Richland, Washington revised 3/8/06 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. p34 Change of base rule for logs: log ln ln a x x a = 9. Circle formula: ( 29 ( 29 2 2 2 x h y k r - + - = 10. Parabola formula: ( 29 ( 29 2 4 x h p y k - = - 11. Ellipse formula: x a y b c a b 2 2 2 2 2 2 1 + = = - 12. Hyperbola formula: x a y b c a b 2 2 2 2 2 2 1 - = = + 13. 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. p581 law of sines: a A b B c C sin sin sin = = 31. p581 law of cosines: 2 2 2 2 cos c a b ab C = + - 32. p581 area of triangle using trig. 1 Area sin 2 ac B = 33. p27 parameterization of ellipse: 2 2 2 2 1 becomes cos , sin x y x a t y b t a b + = = = 34. p57 lim sin x x x 0 1 Hanford High School Calculus Richland, Washington 3 of 11
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35. p67 lim sin x x x →∞ 0 36. p79 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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