Things I Should Know In Calculus Class

Size: px

Start display at page:

Download "Things I Should Know In Calculus Class"

Jonas O’Connor’
5 years ago
Views:

1 Thigs I Should Kow I Clculus Clss Qudrtic Formul = 4 ± c Pythgore Idetities si cos t sec cot csc + = + = + = Agle sum d differece formuls ( ) ( ) si ± y = si cos y± cos si y cos ± y = cos cos ym si si y Doule gle formuls si = si cos cos = cos si cos cos = cos = si Alterte versios of the hlf-gle formuls si( ) = si cos( ) = cos t( ) = t cot( ) = cot + cos cos cos = si = sec( ) = sec csc( ) = csc Slope-itercept form y= m+ poit-slope form y y = m( ) Verticl lie = horizotl lie y = Asolute vlue of umer is the umer = = if 0 d < 0. Grphig trigoometric fuctios f ( ) = si ( c) + d π = mplitude = period c = horizotl shift d = verticl shift Defiitio of the derivtive f ( ) = lim f ( + h) f( ) h 0 h positio velocity ccelertio dow tke derivtive up tke itegrl

2 Thigs I Should Kow I Clculus Clss Cotiuity Test The fuctio y = f( ) is cotiuous t = c if d oly if ll of the followig re true: ) f () c eists ( c is i the domi of f ) ) lim f ( ) eists c ) lim f ( ) = f( c) c d u = u d u d Chi Rule ( ) ( ) Product Rule f ( g ) ( ) + g ( ) f ( ) Quotiet Rule (First times the derivtive of the secod) plus (the secod times the derivtive of the first) du dv v u d u d d = d v v (Bottom times the derivtive of the top) mius (the top times the derivtive of the ottom) over the ottom squred Limit Rules si( h) cos( h) lim = lim = 0 lim 0 h 0 h h 0 h = Derivtives si u = cosudu cosu = siudu t u = sec udu secudu = secu t udu cscudu = cscu cot udu cot udu = csc udu f( f ( )) = f ( f( )) = Horizotl lie test if psses, the fuctio hs iverse. A iverse is determied y iterchgig d y i the fuctio d the solvig the equtio for y. First Derivtive Test. f icreses o I if f ( ) > 0for ll i I. f decreses o I if f ( ) < 0 for ll i I Secod Derivtive Test. Cocve up o I whe f ( ) > 0. Cocve dow o I whe f ( ) < 0. Iflectio poit whe f ( ) = 0or f ( ) fils to eist

3 Thigs I Should Kow I Clculus Clss Symmetry. y-is f ( ) = f ( ). -is f ( ) = f ( ). origi f (, y) = f(, y) origi symmetry cotis d y symmetry -itercepts re zeros of the fuctio The grph of odd fuctio is symmetric with respect to the origi. The grph of eve fuctio is symmetric with respect to the y-is. Asymptotes Horizotl lim f ( ) or. higher epoet i umertor o horizotl symptote. higher epoet i deomitor y = 0. epoets re equl i umertor d deomitor rtio of the coefficiets Verticl zeros of the deomitor Olique (slt) higher epoet must e i the umertor divide the deomitor ito the umertor the quotiet is the symptote Cdidtes for mimum d/or miimum (oe of the followig is true). f ( ) = 0. f ( ) does ot eist. edpoits (if y) of the domi of f L Hopitl s Rule for idetermite forms f( ) 0 lim g ( ) 0 =, if this occurs the f ( ) lim g ( ). Epoetil Growth d Decy A = Ce kt dy ky d = Logistics A y = + Be Akt Trsltios f ( h) shifts f ( ) h uits to the right f ( + h) shifts f ( ) h uits to the left f ( ) + k shifts k uits upwrd f ( ) k shifts k uits dowwrd A closed itervl [, ] cotis the edpoits, ope itervl (, ) does ot.

4 Properties of the turl logrithm Domi: ll positive rels Rge: All Rels Cotiuous Alwys cocve dow Oe-to-oe (iverse is y= e ) l = 0 l e = d l u = du d u Thigs I Should Kow I Clculus Clss y= l Lws of logrithms: l( ) = l + l l = l l l = l Properties of the epoetil fuctio Domi: ll Rels Rge: 0 y > Cotiuous Alwys icresig Oe-to-oe (iverse is e = lim + l e = l e= y = e = l y l e = l e = d u u du e = e d d y = l ) y = e ( e )( e ) e e l = e (, > 0) d d u u du = l = l d d d = e = 4

5 Volume Formuls Coe Sphere 4 π r Thigs I Should Kow I Clculus Clss π Cylider π rectgulr o lwh Surfce Are Formuls Sphere 4π r cylider with closed top π r + Cylider with ope top π r + π Bo with top re of four sides + re of top d ottom Tle of Trigoometric Vlues π Rdis Sie Cosie 0 0 π 6 π 4 π π 0 π 0 - π - 0 5

Important Facts You Need To Know/Review:

Important Facts You Need To Know/Review: Importt Fcts You Need To Kow/Review: Clculus: If fuctio is cotiuous o itervl I, the its grph is coected o I If f is cotiuous, d lim g Emple: lim eists, the lim lim f g f g d lim cos cos lim 3 si lim, t