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Find the Maclaurin series for and its radius of | Ch 11 - 47

Single Variable Calculus | 7th Edition | ISBN: 9780538497831 | Authors: James W Nilsson ISBN: 9780538497831 151

Solution for problem 47 Chapter 11

Single Variable Calculus | 7th Edition

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Single Variable Calculus | 7th Edition | ISBN: 9780538497831 | Authors: James W Nilsson

Single Variable Calculus | 7th Edition

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Problem 47

Find the Maclaurin series for and its radius of convergence. You may use either the direct method (definition of a Maclaurin series) or known series such as geometric series, binomial series, or the Maclaurin series for , , ,

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MotivationandEmotion • Motivesandemotionsmotivateustomove,act,orprepareforaction • ThewordsmotiveandemotionarebothderivedfromtheLatinrootmoveremeaning “tomove” Motivation • Factorsthatactivate,direct,andsustaingoal-directedbehavior • “Why’s”ofbehaviorcannotbeobserved,mustbeinferred • Instincts o Instincttheory:behaviorismotivatedbyfixedinbornpatternsofbehaviorthat arespecifictomembersofaparticularspecies o Problems:listofinstinctsgrewtoolongtobeuseful,instinctsdescribebutdo notexplainbehavior,humanbehavioristoovariableandflexible,whatabout therolesofcultureandlearning • Drivetheory o Maintainthatwearemotivatedbydrivesthatarisefrombiologicalneedsthat demandsatisfaction o Need:stateofdeprivationordeficiency o Drive:astateofbodilytension,suchashungerorthirst,arisingfromanunmet need o Drivereduction:satisfactionofadrive o Homeostasis:tendencytomaintainsteadyinternalstate o Typesofdrives: § Primarydrives:innatedrives,suchashunger,thirst,andsexualdesire, arisingfrombasicbiologicalneeds § Secondarydrives:drivesthatarelearnedoracquiredthroughexperience, suchasthedrivetoachievemonetarywealth • Arousaltheory o Wehaveinnate,biologicalbasedneedforexplorationandactivity § Stimulusmotives:internalstatespromptingexploratorybehavior o Arousaltheory:organismshaveabasicbiologically-basedneedtomaintain stimulationatanoptimallevel o Needsforstimulationvary § Weseekwaystomaintainouroptimallevelofarousal § Strongneedsforhighlevelsofsensation(sensationseeking)appearsto haveastronggeneticcomponent • Incentivetheory o Incentives:thepullsideofmotivation § Rewardsorotherstimulithatmotivateustoact;incentivesmotivateus byexertingapullonourbehavior o Incentivetheory:thebeliefthatourattractiontoparticulargoalsorobjects motivatesmuchofourbehavior § Focusesonthepsychologicalsourcesofmotivation § Holdsthatmotivationisinfluencedbyrewardinggoal-relatedstimuli o Incentivevalue:thestrengthofthepullofagoalorreward • Psychosocialneeds o Needsthatreflectinterpersonalaspectsofmotivation,suchastheneedfor friendshiporachievement o Needforachievement:theneedtoexcelinone’sendeavors § Extrinsicmotivation:reflectsadesireforexternalrewards § Intrinsicmotivation:reflectsadesireforinternalgratification o Primarymotivation § Achievementmotivation:themotiveordesiretoachievesuccess § Avoidancemotivation:themotiveordesiretoavoidfailure • Maslow’shierarchyofneeds:conceptthatthereisanordertohumanneeds,which startswithbasicbiologicalneedsandprogressestoselfactualization selfactualization: fulfillmentofindividual potential esteem: achievement,respect,prestige, status,approval emotionalintimacy,friendships,socialconnections safeandsecurehousing,protectionfromcrimeandharshweather hunger,thirst,avoidanceofpain,sexualgratification,elimination HungerandEating • Thehypothalamus o Lateralhypothalamus:involvedininitiatingeating o Ventromedialhypothalamus:signalswhentostopeating o Neurotransmittersandhormonesalsoplayimportantroles o NeuropeptideY:stimulatesappetiteandeating • Obesity o IntheUS2/3 ofadultsareoverweightand1/3 areobese o IntheUS1/3 ofchildrenareoverweightorobese o Whyisobesityontherise: § Toomanycalories § Toolittleexercise o Casualfactors: § Behavioralpatterns(eatingtoofastortoolargeofportions;adopting unhealthyeatingdiet,eatingfastfoodtoooften) § Genetics § Basalmetabolicrate § Setpointtheory:thebeliefthatthebrainmechanismsregulatebody weightaroundageneticallypredetermined“setpoint” • Heredityinfluencesbodytypeandsetpointandourbodiesalso regulatebycontrollingfoodinputandenergyoutput • Reducingenergyexpendituredropsbasalmetabolicrate:therate ofenergyexpenditureformaintainingbasicbodyfunctionswhen thebodyisatrest § Numberoffatcellsinthebody o Environmentalfactors:exposuretofoodrelatedcues,useofmodernenergy- savingconveniences o Emotionalstates:eatinginanger,toquellanxiety,boredom,etc. o Suggestionsformaintainingahealthyweight § Limitfatintake § Controlportionsize § Slowdownthepaceofeating § Bewareofhiddencalories § Makephysicalactivityapartofyourlifestyle • Eatingdisorders o Anorexia:selfstarvationresultinginanunhealthylowbodyweight § Intensefearofbecomingfat § Distortedbodyimage § Occursmostofteninyoungwomen o Bulimianervosa:characterizedbyepisodesofbingeeatingfollowedbypurging § Obsessedwithweight § Unhappywithbody § Maintainsanormalbodyweight o Causeofeatingdisorders § Socioculturalfactors:thinnessandattractiveness § Psychologicalfactors § Biologicalfactors Emotions • Feelingstatesthatpsychologistsviewashavingphysiological,cognitive,andbehavioral components • Basiccomponentsofemotions o Bodilyarousal:nervoussystemactivation o Cognition:subjectiveexperienceofthefeeling o Expressedbehavior:outwardexpressionofemotions • Sixbasicemotionalexpressions o Anger o Fear § TheJames-Langetheoryproposesthatemotionsfollowbodilyreactions totriggeringstimuli • Perceptionofstimulus⇒arousal⇒emotion § TheCannon-Bardtheoryproposesthatthesubjectiveexperienceofan emotionandthebodilyreactionsassociatedwithitoccurvirtually simultaneously • Perceptionofstimulus⇒arousalandemotion § Thetwo-factormodelproposesthatthecombinationofphysiological arousalandcognitiveappraisal(labeling)ofthesourceofthearousal producesthespecificemotionalstate • Perceptionofstimulus⇒arousaland“I’mafraid”⇒emotion § Thedualpathwaymodelsuggeststwopathwaysforprocessingfear stimuliinthebrain • Ahighroad:theslowerpathleadingtothecerebralcortex • Alowroad:thefasterpathleadingtotheamygdala o Disgust o Sadness o Happiness § Positivepsychology:promotinghappinessbyfocusingonstrengthsand virtues § Emergenceofpositivepsychologyfocusesrenewedattentiononhuman happiness § Twofactorsseemtopredicthappiness:havingfriends,religion • Toincreasepersonalhappiness:gratitudevisits,threeblessings, onedoorclosesandanotheropens,savoring § Threetypesofhappiness:pleasureofdoingthings,gratification,meaning o Surprise • Displayrules:sociallyandculturallyrelatedcustomsregardingtheextenttowhichone outwardlyexpressestheiremotions,varyfromculturetoculture • Facialfeedbackhypothesis o Beliefthatmimickingfacialmovementswillinducethecorrespondingemotion o Duchennesmile:agenuinesmilethatinvolvescontractionofaparticularsetof facialmuscles § Notallsmilesarethesame • Thebrain o Emotionsareregulatedbydifferentareasofthebrain o Thelimbicsystem(includingtheamygdalaandhippocampus)areinvolvedinthe fearresponse o Therearehemisphericdifferencesintheprocessingofemotions • Theypolygraph o Deviceusedtodetectwhetherpeoplearelying o Measuresseveralofthephysiologicalresponsesaccompanyingemotion § Perspiration § Cardiovascular § Breathingchanges o Criticisms: § Lyingdoesnotproduceanydistinctivephysiologicalpattern § Onecanliewithoutanytelltalephysiologicalreaction

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Chapter 11, Problem 47 is Solved
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Textbook: Single Variable Calculus
Edition: 7
Author: James W Nilsson
ISBN: 9780538497831

Single Variable Calculus was written by and is associated to the ISBN: 9780538497831. This full solution covers the following key subjects: Series, maclaurin, known, direct, either. This expansive textbook survival guide covers 11 chapters, and 637 solutions. Since the solution to 47 from 11 chapter was answered, more than 230 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Single Variable Calculus, edition: 7. The answer to “Find the Maclaurin series for and its radius of convergence. You may use either the direct method (definition of a Maclaurin series) or known series such as geometric series, binomial series, or the Maclaurin series for , , ,” is broken down into a number of easy to follow steps, and 39 words. The full step-by-step solution to problem: 47 from chapter: 11 was answered by , our top Calculus solution expert on 11/15/17, 04:21PM.

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Find the Maclaurin series for and its radius of | Ch 11 - 47