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A = 5 2 4 8

Advanced Engineering Mathematics | 7th Edition | ISBN: 9781111427412 | Authors: Peter V. O'Neill ISBN: 9781111427412 173

Solution for problem 10.48 Chapter 10

Advanced Engineering Mathematics | 7th Edition

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Advanced Engineering Mathematics | 7th Edition | ISBN: 9781111427412 | Authors: Peter V. O'Neill

Advanced Engineering Mathematics | 7th Edition

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Problem 10.48

A = 5 2 4 8

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Contemporary Views of Long Term Memory Three Types of Memory System ● Semantic Memory: stores knowledge about the world ○ decontextualized (independent of time and place) ○ how do you know that zebras have stripes ● Episodic Memory: memory of experiences in subjective space and time ○ permits a personal past ○ long term memory of temporarily unique events ○ you remember your 21st birthday better than your lunch last week ○ Autobiographical Memory: usually significant to yourself and forms your personal life history ■ specific, personal, long­lasting ■ late developing (childhood amnesia is the inability for people to form episodic memories before 2­4 years of age) ■ not to be confused with stuff your parents told you that you don’t actually remember ○ Flashbulb Memory: extremely vivid episodic memories ■ usually attached to a surprising, significant, or emotional event ● Procedural Memory: know how to do something rather than knowi​omething ○ sometimes implicit (tacit, nondeclarative) ○ can function without episodic memory ● how to ice skate (procedural) vs. remembering when you learned to ice skate (episodic) vs. knowing ice is frozen water (semantic) What makes memories durable ● Some say repetition but this isn’t always the best (could you describe a penny even though you’ve seen it a thousand times) ● trying to remember what’s on a penny is a recall test which is hard ● recall is much harder than recognition ● clearly repetition is not enough to make this stick permanently in memory ● we can account for this with the Level Processing Theory Levels of Processing Theory ● level or depth of processing (encoding) is the main factor governing storage and retrieval ● long term memory is not simply a permanent storage bin ● basically what you do with a memory after you get it determines whether or not you keep it ● the deeper levels of processing are the ones who make the longest lasting memories ● memory is a byproduct of perceptual/cognitive processing ● superficial processing: leads to poor, short lived memories ● deep, semantic processing: more durable memories ● effort makes no difference ● Evidence for Levels Processing Theory: ○ Maintenance vs. Elaborative Rehearsal ■ repeating something over and over does not mean it will stick around long (this is maintenance or mere repetition) ■ elaborative rehearsal means you elaborate on it (you see an 803 phone number and think “that’s a SC phone number”) ■ mere repetition does not work because all they’re doing is keeping the information in short term memory ○ Repeated exposure may not lead to retention of memory ■ e.g. we have all seen a penny a million times, but we can’t describe it ■ e.g. we have seen a telephone keypad many times but we can’t remember which button goes with each letter ■ in a British study, 0 of 50 adults could put all the numbers and letters on a blank phonepad ○ Incidental Learning is unintentional learning ■ results of surprise memory tests for differently encoded material showed that the deeper the processing required, the more they remembered ■ e.g. when asked to label some words as upper or lowercase, say a rhyme for some words, or put words in a sentence, the deeper the level of processing the more words they remembered ■ e.g. counting consonants in a word vs. putting the word in a category (you remember more of the category words because this requires a deeper level of processing) ■ people wondered if this wasn’t a matter of time (it’s faster to note if something is uppercase than to put it in a sentence) ■ they did structural tests where participants made consonants Cs and vowels Bs (brain = CCBBC) and they did semantic tests asking whether a word fit in a sentence that’s given ■ the structural test took longer than the semantic test but we remembered the semantic task afterwards better ○ Self­Reference Effect: relate something to yourself and you’ll remember it better ■ self­schema: deeper processing of yourself ■ particularly easy to do if someone gives you a list of adjectives to remember and you apply them to yourself ■ we have a lot of deep processing when we think about things related to ourselves ■ think about experiences you have had and you have a lot of memory of these experiences (you can avoid getting a paper cut because you remember what you did the last time you got a papercut) Effects of Context on Memory ○ Encoding Specificity Principle: the probability of remembering depends on similarity of encoding at the time of learning and time of test taking ■ this always happens in a particular context ■ this network of things can help you either remember or not ■ a.k.a. context dependent memory (tendency to remember details about things depends on this match of context) ■ we have an advantage of taking a test in the same room that we learned the material ○ physical context: recall is better in the same physical environment ■ their memory was better tested with the same music they listened to when they studied than if they were tested with different music or silence ○ affective context (mood dependent memory): recall is better when your emotional state at the time of learning and time of recall match ■ i.e. something learned while in a particular mood is best retrieved when in the same mood ■ they took people and made them happy or sad with hypnosis ■ they learned word lists and then were tested while happy or sad ■ there was better memory when the mood was matched ○ Mood Congruence Effect: better memory for material that “fits” your mood ■ e.g. happy people are more likely than depressed people to remember pleasant events ■ don’t confuse this with the mood dependent memory ○ Pollyanna Principle (positivity bias): we tend to have better memory for pleasant material ■ e.g. rosy views of past vacations ■ travelers on a Europeans tour and students on thanksgiving break who went on a trip remembered it as more enjoyable than they said it was at the time ■ in retrospect, the trip becomes more pleasant ■ 61% of the students on a three week bike trip in California said they were disappointed during the trip, but several months later only 11% later remembered they’d been disappointed ○ State Dependent Learning: better memory with the same level/type of drug influence ■ we induce people or animals with drugs and then tested their memory ■ e.g. they had people smoking either cigarettes or weed ■ they used people who volunteered willingly ■ those who were tested under the same drug they used to learn the material did better ■ this does not mean it is a good idea to smoke weed and study and then go to an exam while high Comprehension Effects on Memory ● poor comprehension generally means poor memory ● Power Law of Learning: rate of memory loss decreases over time (basically the forgetting curve) Reconstructive vs. Reproductive Memory ● reconstructive memory: getting the gist is really important ● reproductive memory: basically literal recall ○ our memories are not really like storage bins where we just sticks things away to be remembered ○ we forget stuff, distort stuff, and add stuff in ○ so reproductive memory is not very useful ● Bartlett did studies where he repeatedly tested people’s ability to recall odd stories ○ he gave people English folk tales and asked them to recall them ○ Omissions: people left out information, especially stuff that is illogical or violates expectations ■ e.g. stuff that didn’t really fit in with the story ○ Additions: people added information that would help explain incongruous passages ■ they truly believed this information was in the story in the first place ■ e.g. subjects spent less than a minute in a college office and about a third of them “recalled” books in the room when no books were actually in there ○ Transformations: also called distortions ■ altered information: fishing replaces seal hunting because it’s more familiar ■ altered sequences: people couldn’t always remember the correct order (we often get help with this from semantic memory because we know things like we eat the entree before the dessert) ○ some of the things that were forgotten could be recalled later so stuff isn’t just gone if we can’t remember it at some point in time ● Bartlett was aware that people used their general knowledge about the world to aid them in remembering things ○ he refers to these things as schemas: memories are shaped by an active organization based on past experience or general knowledge ○ e.g. we could describe someone’s visit to a nice restaurant even though we weren’t with them because we know what it’s like ○ schemas: body of organized information we have about a concept, event, or knowledge domain ○ script: type of schema consisting of the knowledge of the typical ordered sequence of events/actions in a particular situation ■ e.g. how you go about getting gas in your vehicle ■ e.g. checking into a hotel ■ basically a schema with a sequence ○ we can try and remember how to get gas by remembering our last trip to the gas station ● linguistic memory: we retain the gist of a passage or sentence rather than the words verbatim ○ seems to be reconstructed from knowledge ● Semantic Integration: we take information from multiple sentences and store it in abstract form ○ in doing this, we no longer remember the exact words ○ we see a couple of sentences taken from a short story and people are basically able to figure out the plot without remembering or ever knowing the exact words of the story Eyewitness Testimony and Face Recognition Studies ● Research done by Loftus ● we’re quite good at recognizing faces we’re familiar with ● however, faulty eyewitness testimony is the most frequent cause of wrongful convictions ● we usually find out that it was wrongful conviction because DNA exonerates people ● these are well­motivated and well­intended witnesses ● Misleading Postevent Information: can distort and transform memories ○ e.g. misleading questions ○ appears that memories themselves are changed, not just people’s reports ○ you could ask “well, just how tall were they” and now the witness thinks they’re tall ● Source Monitoring Confusions: a memory derived from one source may be misattributed to another ○ includes information from before or after a remembered event ○ you may remember something directly but not remember where it came from ○ people remembered meeting Bugs Bunny at Disneyland even though he’s not even Disney ○ they put a clerk from a store that got held up in the line­up and the witness picked him (they got the place right but the source wrong) ● Best Match Criterion: e.g. picking a person from a line­up who most resembles your memory of the culprit ○ a lot of people take the attitude that the culprit is definitely in the line­up, so they don’t feel like they can just say that none of them are right ○ so they pick the person who best matches the culprit and this could be a totally innocent person ● confidence is a poor index of accuracy ● just because someone is confident does not mean they are accurate (this is actually an extremely low correlation) ● Weapons Focus Effect: if there’s a weapon involved in a crime, people find it harder to report on the person ○ we’ve already seen that attention can be really limited and you can see this in crimes involving a weapon ○ our attention is dragged to the weapon and not the person ○ people can often give a really good description of the weapon but then not really be able to describe the person Recovered Memories and False Memory Syndrome ● False Memory Syndrome: involves the belief that a behavioral problem is a reaction to a repressed traumatic event (usually childhood sexual abuse and the development of pseudo memories of childhood trauma) ● there was a lot of this surrounding child caretakers in the 1990s ● it included parents ● this appears to not be about remembering false things, but being led into false memories by someone or something ● accusations of childhood sexual abuse went up like crazy in the 1990s How False Memories can be Induced ● false memories can be induced by suggestion, usually from an authority figure ● Loftus had older siblings tell their little siblings that something had happened to them as a kid ○ the older brother of Chris (14 yo) told him that he got lost in the mall as a kid (this never actually happened) ○ Chris originally gives vague memories like he remembers seeing the stores ○ then after a few weeks of being asked twice a week what he remembers, he starts describing all sorts of details and stuff ● in one study, participants were shown a fake photo of them in a hot air balloon that had been photoshopped from a real photo of them and it led to a vivid recollection of that experience even though they had never actually been in a hot air balloon ● false memories can be induced by dream interpretations because beliefs about one’s past can be readily influenced by a clinician’s dream interpretation ○ dreams may be the “royal road to memory manipulation” ○ studies have found that if you tell someone a dream indicates this particular thing happened to them, they are very confident that it actually happened to them ○ dreams can often later be mistaken for actual events ● Imagination Inflation: imagining events increases the likelihood of believing it happened ○ people can develop both a belief in, and “memory” of, an event that never actually happened to them simply by imagining it occurred ● false memories can be induced by suggestive therapists who may use hypnosis, sodium amytal, dream interpretation, and/or guided imagery ● recovered memories from childhood abuse are more likely to be valid if they occur outside any form of therapy and are a surprise to the victim Causes of Forgetting ● Decay (lack of use): loss of inactive (un­refreshed) memories ○ we forget stuff we don’t use ○ this virtually impossible to test, but theoretically likely to occur ○ forgetting occurs more with episodic memory than with semantic memory ○ we can’t really test this because as time happens other things happen and this leads to interference ● Interference: loss of memory due to other material ○ Proactive Interference: forward acting ■ older memories prevent new facts from being committed to memory ■ e.g. when you learn a new language, your old language may get in the way of your learning ○ Retroactive Interference: backward acting ■ new memories tend to replace old memories ■ e.g. learning a new language could make it difficult to remember an older language ● Amnesia: loss of memory due to trauma or drugs ○ Anterograde Amnesia: something happens and they can’t remember new information (they have a learning deficit) ■ usually their memory span (STM) is normal ■ the memory that exists for them is stuff that happened before the incident ■ this can be temporarily drug­induced (with midazolam) which can be very helpful for research ■ Korsakoff Syndrome often happens to chronic alcoholics and they are likely to suffer memory losses and cannot learn new things ■ H.M. was a famous case where he had a surgery that took out his amygdala and a lot of his hippocampus ● there wasn’t any long term memory for events after the surgery but most of the older memories are intact ● he basically didn’t learn anything new for the rest of his life ■ Clive had a brain infection and he lives every moment in isolation from the past (e.g. minutes after eating a meal, he won’t remember that he ate) ● he remembers a lot such as his wife, how to play piano, how to read, write, and talk ● he feels like he’s always just woken up ○ Retrograde Amnesia: (backwards) no lasting memory of events for a limited period prior to the incident, but information is often retained shortly after the incident and onwards ■ causes include ECT (shock therapy) or head trauma such as concussions ■ how far back it wipes out can be somewhat variable Memory Shifts due to Knowledge or Interference ● knowledge can include environmental variants like momentum or gravity ● we can have shifts in memory just due to stuff we know ● e.g. we know that if you let go of a cup it will fall to the ground ○ if you drop a cup and the lights go out while it’s falling, we will remember the location of the cup in the air as lower than it actually was when the lights went off ● this is representational momentum: memories tend to be distorted in the direction of perceived or implied motion ○ e.g. if we just glance at a bus, we’ll probably remember that it was further down the road than it was ○ these changes match the changes in events (e.g. if the event is faster, the change will be more extreme) ● boundary extension: tendency to remember more of a scene than was actually seen ○ pictures drawn from memory may include elements that would logically fall just outside the boundaries of the original ○ e.g. students saw a picture of a fork and were then asked to recreate it and they drew much more of the fork than was in the picture because they have extensive knowledge of forks Reconstructive Memory: some main points ● memories are rarely exact reproductions of what was experienced; we typically reconstruct memories using inference, beliefs, pre­existing knowledge, and post­event information ● our memories can have distortions and additions as well as errors of omission ● other people may intentionally or unintentionally distort our memories or even implant false memories ● people can have false memories in a variety of situations ● source monitoring problem: we can have problems correctly identifying the source of information in memory ● confidence is not a good indicator of accuracy Methods of Improving Encoding and Consolidation ● consolidation: converting memories from short term to long term memory ● Mnemonics: memory tricks (can be very helpful in acquiring a foreign language vocabulary) ○ Method of Loci: method of locations ■ traceable to a time in ancient Greece when the roof fell in at a banquet and killed all but one man ■ this one man was able to name everybody at the banquet table by the method of loci ■ if you’ve got a set of locations in your mind, you can remember things at those locations and mentally revisit these things and remember things ■ Three steps: identify a sequence of familiar places, create images of to­be­recalled items associated with places, recall by “revisiting” the places ○ Peg Word System: pairs of rhyming words form “pairs” for the to­be­recalled items ■ e.g. #4 is door, #3 is tree, #2 is shoe, etc….. ○ First Letter Technique: acrostics ■ HOMES are the Great Lakes of Michigan ■ ROY G BIV are the colors of the color spectrum ○ Chunking: reducing the amount you need to remember by putting them in chunks ○ Rhyming/Keying: eg. picturing a polka dotted lever to remember that Polk was the eleventh president ● verbal rehearsal (maintenance) doesn’t work nearly as well as mnemonics ● Dual (multiple) encoding: encode things in more than one way and you’ll remember it better ○ Enactment effect: performing actions produces better recall than only learning action phrases ■ e.g. tear the paper ■ combines visual and motor memory ○ you could also combine visual and verbal ○ use varying study environments: college students who studied a list of 40 vocabulary items in two different rooms did far better on the test than students who only studied the list in one room ● comprehension: try to do whatever it takes to understand the material because you’ll remember it better if you comprehend it ● minimize interference: e.g. study before going to sleep ● use distributed vs. massed practice: memory is better when the learning is spread out (spacing effect) ● use deep processing such as elaborative rehearsal ● Self­Test: test yourself on the material before the actual exam ○ testing effect: people who are tested on information and then review how they did and why they missed things will know the information much better ● The goal of these improving retrieval techniques is to recreate types of processing that occurred when the event was originally encoded ○ context reinstatement is a reliable technique ■ e.g. sometimes law enforcement will take the witness back to the scene of the crime ○ a common problem with other techniques is false memories ■ e.g. adults over a long period of time tried to remember the names of schoolmates and there was as steady and significant increase in false names as time went on ○ hypnosis is likely to lead to additional information ■ there may be more recall, but if often won’t be accurate information ■ hypnosis is often used when there is a retrieval problem (they think they saw more than they are able to report) ■ hypnosis increases confidence but not accuracy ■ people are more open to suggestion under hypnosis ● to improve your chances of remembering where you put something, don’t hide it in bizarre or unusual places Prospective Memory ● remembering to do things in the future, as opposed to retrospective memory ● memory for intentions ● Time Based ○ e.g. remember to go to class at 2:00 ○ e.g. remember to take the pie out of the oven ● Event Based ○ e.g. remember to ask a friend about a problem with your car ○ e.g. remember to buy milk on the way home ○ e.g. remember to attach a file to an email ● this is far less studied than retrospective memory, but there are many similarities between the two ○ e.g. impact of retention interval (it is easier to remember to do laundry after class if class ends in an hour as opposed to four hours) ● prospective memory ability appears to be correlated with episodic memory ability ● failures are common and can occur even for highly important events or items and even with a short retention interval ○ departing from your customary action can make these failures more likely ○ being distracted ○ time pressure (you’re in a hurry and you’re likely to forget stuff) ● aging paradox: old people are often more impaired in the laboratory but perform significantly better on time­based tasks than young people in naturalistic settings ○ e.g. make a phone call or take a pill at a certain time ○ this paradox is probably due in part to differences in ongoing task demands in the lab and everyday life Metacognition ● Metacognition is the knowledge and beliefs about cognition, including awareness, understanding, and monitoring of one’s own cognitive state and activities ● Comprehension Monitoring (metacomprehension): understanding how well you understand something ○ this can be really important for students because they need to know if they understand the material in class ○ this is necessary for effective reading ○ failures to spot inconsistencies and contradictions reveal a metacomprehension problem ○ such failures are more common in inexperienced readers ○ a study found that only about half of children spot explicit inconsistencies and almost none spot implicit inconsistencies in stories ○ college students tend to overestimate comprehension and learning and this is a failure of metacomprehension ● Spatial metacognition: e.g. judgement of one’s sense of direction ○ being able to judge if you’re lost or not ○ overall, we have a pretty good metacognition about our sense of direction ○ people who rate rate themselves as having a good sense of direction are usually good at these tasks ■ point in the direction of a known location (e.g. sites on campus) ■ maintaining orientation (e.g. in a maze or underground tunnel system) ● Metamemory: your awareness of how your own memory works (one’s awareness and control of memory processes and capacities) ○ includes knowledge and beliefs about one’s own abilities, judgement of ease of learning, judgement of how well you’ve learned it, and feeling of knowing (tip of the tongue phenomenon) ○ Self Knowledge: type of metamemory where you have some idea of how you compare in memory to people around you ○ Knowledge about differences among tasks (we know it’s easier to remember four numbers than forty) ○ Strategic Knowledge: such as knowing how to use rehearsal and knowing that elaborative rehearsal usually works better than rote quotation ○ You have better metamemory when you: ■ have easy material ■ overlearning/active learning: basically you already know it and you’re going over it again ■ intentional vs. incidental learning (knowing if we’re intentional, we’ll remember it better) ■ feedback: we know self­testing will help us remember something ● General problem with metacognition: we tend to overestimate our performance in comprehension or memory ○ optimistic bias includes both foresight (overestimating future bias) and hindsight bias ○ this can be adaptive, for example if students thought they were going to fail classes, they wouldn’t even take them ○ there is less overconfidence in experts with more experience ○ there is less overconfidence for easy questions Mental Imagery ● mental images are mental representations of objects or events that are not perceptually present ● you can come up with a visual representation even though you can’t actually see it ● e.g. if you think of a frog you can generate an image in your mind ● this is not input from our senses; it is internal and top­down processing ● there’s an ongoing controversy ● some people say mental images are simply epiphenomena which means they are byproducts of other cognitive processes ○ Propositional Hypothesis: all information is coded and stored in propositional form ○ images are created from information stored in the forms of propositions (propositions have a true or false value) ○ and these abstract language­like representations are true or false ○ basically, you know that frogs do or do not have tails ○ the argument is that these images are generated along the way of other cognitive processes ● other people say that the mental images have function somewhat similar to perceiving things ○ they have functional significance ○ Analog Code (pictorial representation) Hypothesis: we can generate images that are analogous (similar but not the same) ○ we can sometimes use mental images like we use real images ○ we can store images away as something other than propositions ● research shows that imagery seems to be able to substitute for perception in many situations ● several perceptual effects are also found in imagery ● imagery can often seem helpful or necessary for solving some problems ○ e.g. people who are experts at an abacus can picture an abacus and do math in their heads by visualizing this ○ it’s hard to argue that mental imagery is just a byproduct based on things like this ● this is supported by the existence of hallucinations which are internally generated images that people mistake for actual perception ● we don’t confuse images for percepts usually because our images are more feeble than actual percepts Imagery Research ● Shepard started this famous research because he had a dream where things were floating around in space so he started examining mental imagery ○ he looked at depictions of 3D objects by presenting them in pairs in people and asking if they are the same ○ he found that people would rotate the objects so they are similarly placed to see if they matched up or not ○ this is called mental rotation ○ reaction time was highly correlated with the degree of rotation, as if the participants were viewing rotating objects and waiting for them to match up so they can compare them ○ participants appear to perform this task by rotating one object until it can be viewed from the same perspective as the reference figure ○ this is very nicely supported by data ○ there are some big individual differences in the ability to do this ○ there was follow up research asking if people can tell if two images are mirror images of each other or not ■ the findings were similar ○ men tend to be better at mental rotation ● Shepard did more research asking people to mentally fold paper ○ asked them, “when folding this pattern into a cube, do these two marked sides meet” ○ this is called mental paper folding ○ we count the number of folds that would need to be made to make the sides meet and there is clear relationship between the number of folds and reaction time ○ there were also experiments where there were patterns on the sides of the cube and participants were asked to choose what the cube would look like when folded up ● people tend to create mental images that are similar in size and other aspects as real life ● image sizing: having mental images that are similar in size to real life ○ there is faster sentence verification for larger images (given people a statement and asking them if it’s true or false) ○ in a larger picture, things are more obvious ● internal psychophysics: the study of how your mental experience relates to the physical world ○ e.g. mental clock example: when asked how far apart the hands are at a certain time, people automatically picture a mental clock face ○ if you cut the lighting in half, people don’t just guess that the light is halved (it’s more complicated than that) ○ people take longer making decisions about things when they are similar to each other ■ symbolic distance effect: when asked which of two animals are larger, it takes longer when the animals are similar in size ■ e.g. mental clocks: we take longer to judge angles of hands on imaged clocks when the hands are closer together ● selective interference: within modality > cross modality ○ more interference from task to another if they involve the same sensory system ○ e.g. visual + visual has more interference than visual + auditory ○ this holds for percept + percept and image + percept ■ people were asked to notice an auditory or visual signal while keeping an auditory or visual image in their mind ■ the best performance is when they are doing two different modalities ● neuropsychology: studies that basically show that part of our brains involving perception are the same parts of the brain with imagery ○ with mental imagery, we use the same parts of the brain we’d actually use to see something (same with auditory) ○ brain damage sometimes produces parallel impairments in imagery and perception ■ e.g. recognizing and visualizing faces (prosopagnosia: face blindness) ■ people that have prosopagnosia might not even recognize their family by facial appearance (they can identify them by other means) ■ people with this also report that they can’t visualize faces ○ neuroimaging has shown many common neural processes underlie perception and depictive imagery ○ so we’re using the same circuits to see stuff and to visualize stuff ■ the fusiform face area is activated when we see faces and when we visualize faces Eidetic Imagery ● a mental image that is so vivid and clear that it is as if it is actually perceived ● eidetikers are usually children and they have images of limited duration ● photographic memory = accurate + detailed + LTM ● there is very little evidence for true photographic memory and some of the research that has been done is suspect ● there was a famous case of a woman who supposedly had a photographic memory and it turns out she was married to the guy doing the research and the author refused to let anyone else examine her. Spatial Cognition ● e.g. Is Detroit or Denver further west ● e.g. Describe exactly how you get to Moe’s from class ● e.g. If you are in a new city, would you rather have accurate verbal directions or a map ● For some people, a survey map can be really confusing and sometimes verbal instructions can be simpler ● However, verbal instructions can be limiting while maps offer more options ● People will pick the way they prefer to get around: verbal or pictorial ● Map have reversibility: if you know A ­> B, then you know B

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Chapter 10, Problem 10.48 is Solved
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Textbook: Advanced Engineering Mathematics
Edition: 7
Author: Peter V. O'Neill
ISBN: 9781111427412

The answer to “A = 5 2 4 8” is broken down into a number of easy to follow steps, and 6 words. The full step-by-step solution to problem: 10.48 from chapter: 10 was answered by , our top Math solution expert on 12/23/17, 04:48PM. This textbook survival guide was created for the textbook: Advanced Engineering Mathematics, edition: 7. Advanced Engineering Mathematics was written by and is associated to the ISBN: 9781111427412. Since the solution to 10.48 from 10 chapter was answered, more than 239 students have viewed the full step-by-step answer. This full solution covers the following key subjects: . This expansive textbook survival guide covers 23 chapters, and 1643 solutions.

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A = 5 2 4 8