Mathematical Notation Math Calculus & Analytic Geometry I

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1 Mthemticl Nottio Mth - Clculus & Alytic Geometry I Use Wor or WorPerect to recrete the ollowig ocumets. Ech rticle is worth poits shoul e emile to the istructor t jmes@richl.eu. 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 istructor use WorPerect 4 pt Times New Rom ot with.75" mrgis, so they my ot look ectly the sme s your ocumet. The equtios were crete usig 4 pt ot. I there is equtio, put oth sies o the equtio ito the sme equtio eitor o iste o cretig two ojects. Be sure to use the proper symols, there re some istces where more th oe symol my look the sme, ut they hve ieret meigs o't pper the sme s wht's o the ssigmet. There re istructios o how to use the equtio eitor i seprte ocumet or o the wesite. 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. I you il to type your me o the pge, you will lose poit. Do't type the hits or the remiers t the ottom o ech pge. These ottios re ue t the egiig o clss o the y o the em or tht chpter. Tht is, the chpter ottio is ue o the y o the chpter test. Lte work will e ccepte ut will lose % o its vlue per clss perio. I I receive your emile ssigmet more th oe clss perio eore it is ue you o't receive ll poits, the I will emil you ck with thigs to correct so tht you c get ll the poits. Ay correctios ee to e sumitte y the ue te time or the origil score will e use. Do't orget to put your me t the top o the pge

2 Chpter - Trigoometry Review Hit: Crete mtri with 5 rows 6 colums to mke this tle Degrees Ris π π π π siθ 3 cosθ 3 tθ 3 3 ue θ π θ π + θ π θ si si cos cos t = t A gle i QI ecomes i QII, i QIII, i QIV. ( ) = ( ) = si + cos = + t = sec cot + = csc si π cos cos π si t π = = = 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 = Do't orget to put your me t the top o the pge

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. ( ) = m m = m m + m + + m + Deiitio o Limit i wheever. = L Commo Trigoometric Limits ε >, δ > L < ε < < δ si cos t = = = = A uctio is cotiuous t i ) is eie, ) eists, 3) =. ( ) I is cotiuous o [,] k is etwee, the there eists t lest [, ] = k oe such tht. Do't orget to put your me t the top o the pge

4 Chpter 3 - Derivtives These o't hve to e lige like this, I just i it so it woul it o oe pge. y Nottio ( ) = ( ) = D ( ) = = y y ( ) = ( ) = D ( ) = = y = = Deiitio ( ) ( ) ( + ) h 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 + Δ Do't orget to put your me t the top o the pge

5 Chpter 4 - Applictios o the Derivtive ( ) > ( ) < I is ieretile, the is icresig whe, ecresig whe, ( ) = costt whe. ( ) = ( ) ( ) Criticl poits occur where or is ueie. Sttiory poits re the = criticl poits where. I is twice ieretile, the is cocve up whe ( ) < whe. ( ) > cocve ow Ilectio poits occur whe cocvity chges. This c occur whe ( ) is ueie. Reltive etrem c oly occur t criticl poits. ( ) = or = = 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 () () () Do't orget to put your me t the top o the pge

6 Chpter 5 - Itegrtio = + + = + C ( ± ) = ± k k k k k= k= k= * ( k) = Δ m Δ 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 Do't orget to put your me t the top o the pge

7 Chpter 6 - Applictios o Itegrtio To get the I symol to grow with the itegr, hol ow the shit key whe selectig it rom the meu. Are etwee two curves right A = g = top ottom Volume o soli o revolutio out -is usig isk metho V = π Volume o soli o revolutio out -is usig wsher metho let ( ) V = π g Volume o soli o revolutio out y-is usig cyliricl shell metho V = π Legth o ple curve y L= + t t t Are o surce o revolutio (-is) π y S = + Averge Vlue = ve Work W = F Flui Force F = ρ h w Do't orget to put your me t the top o the pge