Things I Should Know Bfor I Gt to Calculus Class Quadratic Formula = b± b 4ac a sin + cos = + tan = sc + cot = csc sin( ± y ) = sin cos y ± cos sin y cos( + y ) = cos cos y sin sin y cos( y ) = cos cos y + sin sin y sin = sin cos cos cos sin = cos = cos cos = sin cos + cos = sin cos = sin( ) = sin( ) cos( ) = cos( ) slop-intrcpt form y=m+b point=slop form y y = m vrtical lin quation =a ( ) horizontal lin quation y=b Absolut valu of a numbr is th numbr = = if is gratr than or qual to 0 and if < 0
f ( ) = a sin b ( c ) + d a = amplitud = priod b c =horizontal shift d =vrtical shift f ( ) = lim f ( + h ) f ( ) h 0 h position vlocity acclration down-tak a drivativ up tak an intgral lim = 0 Continuity Tst Th function y = f() is continuous at =c if and only if all of th following ar tru: ) f(c) ists (c is in th domain of f) ) th limit as approachs c of f() ists ) th limit as approachs c of f() = f(c) Chain Rul d n ( u ) = ( n ) u d n du d Product Rul First tims th drivativ of th scond plus th scond tims th drivativ of th first. Quotint Rul du dv v u d u d d = d v v Bottom tims th drivativ of th top minus th top tims th drivativ of th bottom.
sinh lim = h 0 h cosh lim = 0 h 0 h Drivativs sin u = cos udu cos u = sin udu tan u = sc sc u = sc u tan udu csc u = csc u cot udu cot u = csc udu udu f ( f ( )) = f ( f ( )) = dtrmin th invrs of a function by intrchanging and y and solving for y. First Drivativ Tst. f incrass on I if f ( ) > 0 for all in I. f dcrass on I if f ( ) < 0for all in I Scond Drivativ Tst. Concav up on I whn y > 0. Concav down on I whn y < 0. Inflction point y = 0 or y fails to ist Symmtry y-ais f(-)=f() -ais f(-) = - f() origin f(-,-y)=f(,y) origin symmtry contains and y symmtry
horizontal asymptot lim f ( ) OR. highr ponnt on top no horizontal asymptot. highr ponnt on bottom y=0. Eponnts sam ratio of cofficints Vrtical asymptots zros of th dnominator Candidats for maimum and minimum (on of th following is tru). f ( ) =0. f ( ) dos not ist. ndpoints (if any) of th domain of f L Hopital s Rul for indtrminat forms f ( ) 0 f ( ) lim = if this occurs thn lim a g ( ) 0 a g ( ) Proprtis of y= ln() Domain: all positiv rals Rang: all Ral numbrs Continuous Always concav down On-to-on (has an invrs) Ln = 0 Ln = d ln u d = du u d ln( ab ) = ln a + ln b a ln = ln a ln b b n ln a = n ln a 4
Proprtis of y = = lim + n n n n ln = n ln = n y = = ln y ln = ln = d d u = u du d invrs of ln Domain: all ral numbrs Rang: y > 0 Continuous Always incrasing = ( )( ) = a = ln a d a = a ln a d d u u du a = a ln a d d a a > 0 5
Eponntial Growth and Dcay -intrcpts ar zros of th function A = C kt dy ky d = Translations f(-h) shifts f() h units to th right f(+h) shifts f() h units to th lft f() + k shifts f() k units upward f()-k shifts f() k units downward Th graph of an odd function is symmtric about th origin. Th graph of an vn function is symmtric about th y-ais. Horizontal lin tst if passs, th function has an invrs. A closd intrval [, ] contains th ndpoints, an opn intrval (, ) dos not. Volum Formulas Con Cylindr r h Rctangular bo lw h sphr r h 4 r Surfac ara Sphr 4 r bo with a top ara of four sids + ara of top and bottom cylindr with closd top r + rh cylindr with opn top r + rh Trigonomtric Idntitis tan= sin cot= cos sc=. csc=. cos sin cos sin 6
Tabl of Trigonomtric Valus Radians Dgrs Sin Cosin 0 0 0 6 0 4 45 60 90 0 80 0-70 - 0 7