Mathematical Notation Math Calculus & Analytic Geometry I

Transcription

1 Mthemticl Nottio Mth - Clculus & Alytic Geometry I Nme : Use Wor or WorPerect to recrete the ollowig ocumets. Ech rticle is worth poits c e prite give to the istructor or emile to the istructor t jmes@richl.eu. I you use Microsot Works to crete the ocumets, the you must prit it out give it to the istructor s he c t ope those iles. Type your me t the top o ech ocumet. Iclue the title s prt o wht you type. The lies rou the title re't tht importt, ut i you will type t the egiig o lie hit eter, oth Wor WorPerect will rw lie cross the pge or you. For epressios or equtios, you shoul use the equtio eitor i Wor or WorPerect. The ocumets were crete usig 4 pt Times New Rom ot with str mrgis. For iiviul symols (:, F, etc), you c isert symols. I Wor, use Isert / Symol choose the Symol ot. For WorPerect, use Ctrl-W choose the Greek set. There re istructios o how to use the equtio eitor i seprte ocumet. Be sure to re through the help it provies. There re some emples t the e tht wlk stuets through the more iicult prolems. You will wt to re the hout o usig the equtio eitor i you hve ot use this sotwre eore. These ottios re ue t the egiig o clss o the y o the em or tht uit. Tht is, the uit ottio is ue o the y o the uit test. Lte work will e ccepte ut will lose % per clss perio.

2 Chpter - Trigoometry Review Degrees Ris π π π π siθ 3 cosθ 3 tθ 3 3 ue si cos = t = sec cot = csc π π π si = cos cos = si t = cot cos ± = coscos si si si ± = si cos± cossi t t ± t ± = tt ( ) t = = = t cos cos si si si cos t cos cos cos = si =

3 Chpter - Limits Whe iig iite it, simply sustitute the vlue ito the epressio uless it cuses prolems. The two sie it ( ) ( ) ( ) eists i oly i oth oe sie its eist re equl to ech other. I rtiol uctio hs it o the orm /, the there is commo ctor i oth the umertor the eomitor. Fctor oth, reuce, the evlute the it. Whe iig iiite its o polyomil rtiol uctios, oly the leig term ees to e cosiere. This is oly true or its s or. Tht is... ( ) ( " = ) " = m m m m m " m L < < δ. = i ε >, δ > L < ε wheever si cos t = = = = ( ) A uctio is cotiuous t i ) is eie, ) eists, = 3). ( ) I is cotiuous o [,] k is etwee, the there eists t [, ] = k lest oe such tht.

4 Chpter 3 - Derivtives y = = D = = y y ( ) = ( ) = D ( ) = = y Nottio = = h Deiitio ( ) ( ) ( ) h h Power Rule = Prouct Rule [ ] g = g g g g = g g Quotiet Rule Chi Rule Trigoometric Fuctios ( g ) = ( g( ) ) g ( ) y y u = u [ si ] = cos [ t ] = sec [ sec ] = sec t [ cos ] = si [ cot ] = csc [ csc ] = csc cot Locl Lier Approimtio

5 Chpter 4 - Applictios o the Derivtive I is ieretile, the is icresig whe ( ) <, costt whe ( ) =. ( ) >, ecresig whe ( ) = ( ) ( ) = Criticl poits occur where or is ueie. Sttiory poits re the criticl poits where. I is twice ieretile, the is cocve up whe ( ) < ow whe. ( ) > cocve = Ilectio poits occur whe cocvity chges. This c occur whe or ( ) is ueie. Reltive etrem c oly occur t criticl poits. = = I is twice ieretile t, the there will e reltive = > = miimum t i reltive mimum t i <. I =, the seco erivtive test is icoclusive. Rectilier Motio Positio st () Velocity vt () s () t Spee () s = = t s spee = v t = t v s t = v t = = s t = t t Accelertio () () ()

6 Chpter 5 - Itegrtio = = C ( ± ) = ± k k k k k= k= k= * ( k) = m k k = k = = = c c I is cotiuous o [,] F is y tierivtive o o [,], the = = F F F I is cotiuous = F () t t = t t is tierivtive o, the = ve

7 Chpter 6 - Applictios o Itegrtio Are etwee two curves A= g Volume o soli o revolutio y isk metho (-is) V = π Volume o soli o revolutio y wsher metho (-is) ( ) V = π g Volume o soli o revolutio y cyliricl shell metho (y-is) V = π Legth o ple curve y L= t t t Are o surce o revolutio (-is) S = π Work W = Flui Force F F = ρ h w