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Calc Formula Sheet

# Calc Formula Sheet - AP CALCULUS FORMULA LIST 1 Definition...

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AP CALCULUS FORMULA LIST Definition of e: 1 lim 1 n n e n °± ² ³ = + ´ µ · ______________________________________________________________________________ Absolute value: 0 0 x if x x x if x ¸ ¹ = º » < ¼ ______________________________________________________________________________ Definition of the derivative: ( ) ( ) 0 ( ) lim h f x h f x f x h ° + » ½ = ( ) ( ) ( ) lim x a f x f a f a x a ° » ½ = » (Alternative form) ____________________________________________________________________________ Definition of continuity: f is continuous at c iff 1) f ( c ) is defined; 2) lim ( ) exists; x c f x ° 3) lim ( ) ( ). x c f x f c ° = _____________________________________________________________________________ ( ) ( ) Average rate of change of ( ) on [a, b] = f b f a f x b a » » _____________________________________________________________________________ Rolle's Theorem: If f is continuous on [ a , b ] and differentiable on ( a , b ) and if f ( a) = f ( b ), then there is at least one number c on ( a , b ) such that ( ) 0. f c ½ = _____________________________________________________________________________ Mean Value Theorem: If f is continuous on [ a , b ] and differentiable on ( a , b ), then there exists a number c on ( a , b ) such that ( ) ( ) ( ) . f b f a f c b a » ½ = » ______________________________________________________________________________ Intermediate Value Theorem: If f is continuous on [ a , b ] and k is any number between f ( a ) and f ( b ), then there is at least one number c between a and b such that f ( c ) = k . _____________________________________________________________________________ 2 2 2 2 sin 2 2sin cos cos sin cos 2 1 2sin 2cos 1 x x x x x x x x = ¹ » ¾ = » º ¾ » ¼ 2 2 1 cos2 cos 2 1 cos2 sin 2 x x x x + = » =

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[ ] 0 d c dx = 1 n n d x nx dx » ¿ À = Á Â [ ] d uv uv vu dx ½ ½ = + 2 d u vu uv dx v v ½ ½ » ¿ À = Ã Ä Á Â ( ) ( ) ( ) ( ) ( ) d f g x f g x g x dx ¿ À ½ ½ = Å Á Â [sin ] cos [cos ] sin d du d du u u u u dx dx dx dx = = » 2 2 [tan ] sec [cot ] csc d du d du u u u u dx dx dx dx = = » [sec ] sec tan [csc ] csc
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Calc Formula Sheet - AP CALCULUS FORMULA LIST 1 Definition...

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