Problem 16E

Problem

Show that for a differentiable function p(t), we have

which is the basis of the centered difference approximation used in (20).

BY124 Dr.Cusic 1/12/16 ExamI 1. Plantcelloverview a. Eukaryotic b. Multicellular c. Autotrophic(maketheirownfoodthroughphotosynthesis) d. ContainchlorophyllsA(mainone),B(givesgreencolor), e. Containcarotenoids(red/orangethatappearinautumn) f. Storeglucoseasstarch g. CellwallsmadeofthecomplexcarbohydrateCellulose h. Havealargecentralvacuoleforstorage i. Communicateusingplasmodesmata 2. Landplants a. Evolvedaround500millionyearsago b. Evolvedfromcharophytes i. Charophytesareatypeofgreenalgae c. Ancestralalgae i. Redalgae ii. Chlorophytes iii. Charophytes iv. Embryophytes d. AlgaeandCharophyteSimilarites i. Bothhavecircularringsofcellulosesynthesizingprotein ii. Flagellatedsperm(notinalllandplantsthough) iii. Formationofphragmoplasts 1. Phragmoplastsaremicrotubulesthataidinformingthecellplate iv. Haveasporopolleninpolymer 1. Usefulwheninorganismisindangerofdryingout e. Differencesincharophytesandplants i. ApicalMeristems 1. Theseareundifferentiatedtissuesusedforgrowth ii. Alternationofgenerations 1. Diploid(2n)sporophyteundergoesmeiosistoproducehaploid(n) sporesthatbecomeahaploid(n)gametophyte.Thegametophyte undergoesmitosistoproducehaploid(n)gameteswhichfertilize andgrowintoadiploid(2n)sporophyte. 2. Asporeisacellthatwillgrowbymitosisintoamulticellular organismwithoutfusingwithanothercell a. Sporesproducehaploid(n)gametophytes. iii. Wallsporesinthesporangium 1. Actasaprotectivecovertopreventdryingout iv. Multicellulargametangia 1. Archegoniummakeseggs 2. Antheridiummakessperm v. Multicellulardependentembryos 1. Containedinarchegonium 2. Haveplacentatransfercellsfornutrients