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514. Shell method Let R be the region bounded by the

Calculus: Early Transcendentals | 2nd Edition | ISBN: 9780321947345 | Authors: William L. Briggs ISBN: 9780321947345 167

Solution for problem 5 Chapter 6.4

Calculus: Early Transcendentals | 2nd Edition

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Calculus: Early Transcendentals | 2nd Edition | ISBN: 9780321947345 | Authors: William L. Briggs

Calculus: Early Transcendentals | 2nd Edition

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Problem 5

514. Shell method Let R be the region bounded by the following curves. Use the shell method to find the volume of the solid generated when R is revolved about the y-axis. y = x - x2, y = 0 y _ x _ x2 0 y 1 x

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2.0.4. Working Memory I (Short Term vs. Long Term) William James: Postulated 2 forms of memory Primary Memory (Short term & working memory)  Immediately Available  Limited Capacity  Effortlessly available yet fleeting  Increased neural firing relative to baseline  Consistently active nodes Secondary Memory (Long term memory)  Memories of the past  Permanent, but available only with effort  Unlimited capacity  nodes are inactive until triggered  Slower access  Unit-to-unit changes in synaptic connections or the strength of these connections Donald Hebb (Hebbian Learning) STM relies on temporary activation; LTM relies on structural changes in neurons/connections. “Neurons that fire together, wire together.” Modal Model of Memory Sensory → Short Term Memory ⇔ Long Term Memory (storage) (loss) (loss) (possible decay/interference) Span Task: Lists of increasing number of items. What is measured is the number of items in the list that people recall correctly 50% of the time. George Miller: “Magic #7” On average, people can keep about 7 things in memory at a time (without practice) Chunks: A unit of knowledge that organizes together a few sub-items. Usually remembering one part of a chunk helps you remember the rest of it. (chunking capitalizes on LTM)  span increases by increasing the number of items in a chunk Chase & Ericson: Chunking experiment in which they gave an average test subject practice with longer lists of digits. Increased his recall to 80 digits. Primacy Effect: Good recall for the first things seen or heard (employs LTM) Recency Effect: Good recall for things seen/heard last (Items are still in STM) Recency Effect is affected with delay since items leave STM. The Primacy Effect is impaired in amnesic patients (because they have trouble with recall) There is a double dissociation: STM & LTM depend on different processes Evidence for For Primacy & Recency related things. Patients H.M & E.P: Intact STM but heavily impaired LTM. Patient EP was able to repeat lists of words, but could not do so 10 minutes later. (These people lived in the present) Patients K.F & E.E: Intact LTM but impaired STM.  Patient K.F had lesions in the left temporal/parietal region. He had a limited span for auditory material.  E.E had a tumor in his left angular gyrus. He had poor STM fir abstract verbal material (words with no specific meaning).\ What implications does this have for the Modal Model  It implies that short term memory is a gateway to long term memory  Evidence against hierarchical structure  Rote rehearsal yields poor LTM. Things done stick if you don't assign some meaning or attention to them. Levels of Processing Craik & Lockhart: During reading, we process:  Perceptual features (details)  Phonological features (What things sound like)  Semantic features (what they mean) We have better memory for things with deep semantic processing Our STM & LTM are separate entities and what not, but they must interact with each other. We call this WORKING MEMORY Baddeley & Hitch: “Working memory” to describe interaction between LTM & STM. It is a system for maintaining & manipulating our active representations. Patient P.V: Severely impaired STM. Could not do mental math. Patient K.F: Memory span for visually presented letters was better than auditory span. Patient E.L.O: Suffered a stroke to right fronto-temporal region.  He had a severe deficit for visuospatial working memory, But auditory working memory was normal. Double Dissociation between patients KF & ELO. Suggests working memory is not a unitary system. Working Memory Model (Baddeley) Tripartite Model combines processing & storage. There are two storage buffers; Phonological Loop & Visuospatial Sketchpad. One Central Executive that manages attention & coordinate stores (no actual storage capacity, it just manages shit yall) The Phonological Loop Phonological store: A short term phonological store that is responsible for storing auditory memory traces that are subject to rapid decay. Phonological Rehearsal: Accesses & maintains representations through subvocal rehearsal (repeating something to yourself inside of your head) Phonological Similarity Effect: Words that sound similar to each other are harder to remember than words with distinct sounds.  Semantic Similarity seems to have little effect on recall, which suggests that information is coded largely phonologically in working memory. Word Length Effect: Verbal span decreases w/ the number of syllables per word.  left fronto-parietal area activation. (greater activation for words with longer syllables) Articulatory Suppression: PL is disrupted by overt or covert articulation of irrelevant phonological codes.(Someone talking to you while trying to do a task) Separating rehearsal from storage More activation in left frontal regions in the “2-back” task than w/ the search control task.  Left frontal lobe= rehearsal  Left Parietal= Storage There are separate rehearsal & storage processes in PL Visuospatial Sketchpad Pre-frontal cortex is necessary for spatial working memory (determined by animal lesion studies). Monkey studies of working memory Delayed response Task  Impaired by lateral PFC lesion Associative Delayed Match to Simple Task  Not impaired by lateral PFC lesions but rather by MTL lesions. Oculomotor Delayed Response Task: A sample stimulus is presented,delay, cue is given,then a saccade must be made. There is persistent activity in the PFC during the delay task (keeping the task in mind). Activation in the frontal eye fields is positively correlated w/ memory guided saccade accuracy. 2.0.5. Working Memory II Working Memory II Frontal-Posterior Circuits Complex cognitive processes like working memory involve widespread networks of cortical brain areas where component processing is distributed. ex. broca’s area, frontal eye fields There isn't one part of the brain that ‘“Does working memory”. The frontal cortex plays a role but it’s not just that. Proposed that there are circuits between frontal and posterior regions that help with working memory Dorsal circuits =spatial memory/ location (“Where” pathway) Posterior parietal cortex connects to dorsolateral prefrontal cortex Ventral circuits = object memory (“what” pathway) posterior temporal cortex connects to prefrontal cortex.  Processing in more posterior regions is important for perception and are recruited in working memory.  when we are using working memory, it’s through the activity in this circuitry. Allows us to keep things in mind. Evidence “what” and “where” in PFC neurons Can we find neurons that fire more to “What” vs “Where” Single cell recordings in monkeys. “What” (Ventral Stream)= learning which object to focus on “Where”(Dorsal)= learning where that object went in space If the monkey passively viewed the stimuli then there is no differential response to one stimuli. Only in the context of the working memory task did we see difference in response. so the PFC neurons are firing in service of some goal, so they are representing the task at hand. (Firing patterns can change with varying tasks) Connections between goal representations (PFC) and long term memory representations (posterior regions) PFC is representing the goals rather than the long term representations themselves. For example, patients with damage to PFC do not have long term memory impairments. That’s b/c those PFC parts aren't storing these long term representations. PFC & FFA Activation during face working memory task. Seeing a series of faces, delay, and then retrieval cue. PFC activation remains high during delay (keeping the task/goal in mind) Magnitude of activation with the number of faces that the person had in Working memory (WM works harder).FFA Activation dropped off during delay but remains above baseline. Activity also peaked for both areas during encoding and retrieval but more so in FFA. Category Specific Activation during WM Maintenance. Two types of recognition tasks, face and houses (FFA and PPA) See face, delay, recognize face. results show peak during encoding and retrieval and maintenance during delay (FFA) Working Memory Model - Baddeley & Hitch Is WM a system sub served by different brain areas or emergent property ( Might be more useful) that is activated by long term representations  Emerges from the way the mind works, the way the PFC keeps a goal in mind and activates long term representations. Are there processing differences across the PFC; are there different parts that can do different things Dorso-lateral(DLPFC) vs. Ventro-lateral(VLPFC) Pre-Frontal Cortex  Ventrolateral PFC activates and retrieves representations in posterior cortex. It maintains these representations. (keeping an answer in your head)  Dorsolateral PFC manipulates representations and enables goal attainment often for complex goals.. (mental math) Maintenance vs. Manipulation distinction Evidence: Vary the nature of the working memory task (Whether its verbal or spatial) and the direction they have to keep info in mind.  The VLPFC shows similar results during the forward and backward portions of this task because participants are maintaining the same amount of info.  DLPFC response was increased because patients have to manipulate information in the backwards tasks differently. n-Back Task: Involves both maintenance and manipulation  DLPFC Activation increases with increasing n-back difficulty Hypotheses of how PFC is organized in service of working memory Hierarchical organization of PFC: 3 of the proposed gradients that may exist in PFC O’Reilly 1. Ventral-Dorsal Distinction: Maintenance vs Manipulation 2. Anterior-Posterior Distinction: more involved in abstract vs concrete representation  Premotor cortex activation increased with number of stimulus response mappings  Caudal lateral PFC activation increased w/ contextual demands. (responding to one situation in specific)  Rostral lateral PFC activation increased when rules changed from one block to the other (Rule reversal) 3. Lateral-Medial Distinction external vs internal(thoughts) information Can we improve our Working Memory With intensive training, we can be as good as chimps with working memory! Challenging 2 back task mixed with an auditory task. With more practice, people got better at doing it. People who practiced longer did better. But does this actually translate to anything useful outside of that task They measured Fluid Intelligence, which is thinking creatively and abstractly, solving problems (Opposite of Crystallized Intelligence)  Raven’s Progressive Matrices there was a gain in terms of Fluid Intelligence based on the amount of training they had in the n- back tasks. So it’s possible. Information gleaned from Quiz Practice Questions Local- Global Stimuli: The right hemisphere identifies global targets more quickly than the left hemisphere. (An “M” made of letter “F’s”). Left hemisphere is more specialized for more local processing. If this were split brain patients, and something were presented to Left visual field, they would deny seeing it. Posner spatial cueing task. A flash of light correctly cues the location of an upcoming target, and enhanced the participants reaction time to detect that target. However objects that appear in that position again will be temporarily inhibited due in part to Inhibition of Return. We don't return attention back to things we’ve already attended to. Delayed-Response Task tests working memory. Maintaining something in mind over a short delay. (NOT LIKE A DAY LATER) Someone with isolated retrograde amnesia most likely has damage to MTL causes ANTEROGRADE Amnesia, and temporally graded retrograde amnesia but not really as severe as JUST retrograde. The damage is most likely to anterior lateral temporal lobes. (regions may play a role in retrieving stored long term memory) Balint’s Syndrome is caused by BILATERAL DAMAGE to posterior parietal & occipital damage. Simultanagnosia, Ocular, Apraxia, Optic Ataxia.

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Textbook: Calculus: Early Transcendentals
Edition: 2
Author: William L. Briggs
ISBN: 9780321947345

This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 2. The full step-by-step solution to problem: 5 from chapter: 6.4 was answered by , our top Calculus solution expert on 12/23/17, 04:24PM. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321947345. This full solution covers the following key subjects: . This expansive textbook survival guide covers 128 chapters, and 9720 solutions. The answer to “514. Shell method Let R be the region bounded by the following curves. Use the shell method to find the volume of the solid generated when R is revolved about the y-axis. y = x - x2, y = 0 y _ x _ x2 0 y 1 x” is broken down into a number of easy to follow steps, and 49 words. Since the solution to 5 from 6.4 chapter was answered, more than 261 students have viewed the full step-by-step answer.

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514. Shell method Let R be the region bounded by the