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formula152spring08final

# formula152spring08final - Formula Sheets for the Math 152...

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Formula Sheets for the Math 152 Final Exam The solutions of ax 2 + bx + c = 0 are x = ( - b ± b 2 - 4 ac ) / (2 a ). e a + b = e a e b , ln( ab ) = (ln a ) + (ln b ) , ln( a b ) = b (ln a ) , ln(1) = 0 , ln( e ) = 1 e ln x = x , ln( e x ) = x , d dx ( e x ) = e x , d dx (ln x ) = 1 /x , R du u = ln | u | + C sin(0) = 0 , sin( π/ 6) = 1 / 2 , sin( π/ 4) = 2 / 2 , sin( π/ 3) = 3 / 2 , sin( π/ 2) = 1 cos(0) = 1 , cos( π/ 6) = 3 / 2 , cos( π/ 4) = 2 / 2 , cos( π/ 3) = 1 / 2 , cos( π/ 2) = 0 tan x = sin x/ cos x , cot x = cos x/ sin x , sec x = 1 / cos x , csc x = 1 / sin x cos 2 x + sin 2 x = 1 , 1 + tan 2 x = sec 2 x , 1 + cot 2 x = csc 2 x sin A cos B = (1 / 2)[sin( A - B ) + sin( A + B )] sin A sin B = (1 / 2)[cos( A - B ) - cos( A + B )] cos A cos B = (1 / 2)[cos( A - B ) + cos( A + B )] sin(2 x ) = 2sin x cos x , cos(2 x ) = cos 2 x - sin 2 x cos 2 x = (1 / 2) ( 1 + cos(2 x ) ) , sin 2 x = (1 / 2) ( 1 - cos(2 x ) ) d dx (sin x ) = cos x , d dx (tan x ) = sec 2 x , d dx (sec x ) = sec x tan x d dx (cos x ) = - sin x , d dx (cot x ) = - csc 2 x , d dx (csc x ) = - csc x cot x d dx (sin

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formula152spring08final - Formula Sheets for the Math 152...

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