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

Fundamentals of Differential Equations | 8th Edition | ISBN: 9780321747730 | Authors: R. Kent Nagle, Edward B. Saff, Arthur David Snider ISBN: 9780321747730 43

Solution for problem 16E Chapter 3.2

Fundamentals of Differential Equations | 8th Edition

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Fundamentals of Differential Equations | 8th Edition | ISBN: 9780321747730 | Authors: R. Kent Nagle, Edward B. Saff, Arthur David Snider

Fundamentals of Differential Equations | 8th Edition

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Problem 16E

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).

Step-by-Step Solution:
Step 1 of 3

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

Step 2 of 3

Chapter 3.2, Problem 16E is Solved
Step 3 of 3

Textbook: Fundamentals of Differential Equations
Edition: 8
Author: R. Kent Nagle, Edward B. Saff, Arthur David Snider
ISBN: 9780321747730

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