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Prove that if n is a positive integer, then 7n 2 1 is

Calculus | 8th Edition | ISBN: 9781285740621 | Authors: James Stewart ISBN: 9781285740621 127

Solution for problem 17 Chapter 1

Calculus | 8th Edition

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Calculus | 8th Edition | ISBN: 9781285740621 | Authors: James Stewart

Calculus | 8th Edition

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Problem 17

Prove that if n is a positive integer, then 7n 2 1 is divisible by 6.

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Ch 5 Book notes 02/24/2016 ▯ Perceptual organization  process by which elements in the environment become perceptually grouped to create our perceptions of objects  involves 2 components o grouping and segregation ▯ Gestalt  Gestalt psychologists- “are configurations formed from smaller elements”, the whole is different than the sum of its parts  Before gestalt principles was William Wundt who studied structuralism (distinguished between sensations, elementary processes that occur and perceptions)  Gestalt psychologist reject that perceptions were formed by adding up sensations and that past experience played a role in perception The principle of good continuation o when connected result in straight or smoothly curving lines are seen as belonging together o also when an object is covered it is still seen as connected to the part that is covered Principle of Pragnanz/Principle of good figure/Principle of simplicity o This is the central theory of gestalt psychology  Every stimulus pattern is seen in such a way that the resulting structure is as simple as possible  Ex. Olympic cirlces is seen as 5 cirlces not parts even though they over lap Principle of similarity o Similar things appear to be grouped together Principle of proximity o Things that are near each other tend to be grouped together Principle of common fate o Things moving in the same direction appear to be grouped together  One image based factor proposed was that area lower in the field are more likely to be perceived ▯ Perceiving scenes and objects in scenes  one way to distinguish between objects and scenes is that objects are compact and are acted “upon”, scenes are extended in space and are acted “within”  ex. If we go out to mail a letter, the mailbox is what we are acting upon and the street is where we are acting within The role of inferencing  people use their knowledge of physical and semantic regularities such as the ones we have been describing to infer what is going on  process by which elements in the environment become perceptually grouped to create our perceptions of objects  FFA ( fusiform face area)- in the temporal lobe and recognizes faces  PPA (parahippocampal place area)- fires when other stimuli besides faces are present ▯ Faces  The part of the brain that is responsible for emotional reaction to the face is located in the amygdala  Evaluation of where a person is looking is the superior temporal sulcus, this area is also responsible for perceiving movements of a persons mouth  Evaluating persons attractiveness is the frontal lobe ▯ ▯ Key terms: ▯ Inverse projection problem: the task of determining the object responsible for a particular image on the retina, it involves starting with the retinal image and extending rays out from the eye ▯ Viewpoint invariance: ability to recognize an object seen at different viewpoints ▯ Perceptual organization- process by which elements in the environment become perceptually grouped to create our perceptions of objects ▯ Grouping- is the process by which visual events are pit together into units or objects ▯ Separation- the process of separating one area or object from another ▯ Structuralism- is when sensations combine to create a perception. For example the picture in the book with the drawing of the face, structuralism sees the first point as the dots that end up creating the full picture. Another principle is also that the combination of sensations to form perception is aided by the observers past experience ▯ Reversible figure- ground- figure can be perceived as both the figure and the ground ▯ Scene- is a view of a real world environment that contains background elements and multiple objects that are organized in a meaningful way relative to each other and the background ▯ Physical regularities- are regularly occurring physical properties of the environment. For example there are more physical and vertical and horizontal orientations in the environment ▯ Structural encoding- based on the relationship between voxel activation and structural charcteristics of a scene, such as lines, contrasts, shapes and textures ▯ ▯ ▯

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Chapter 1, Problem 17 is Solved
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Textbook: Calculus
Edition: 8
Author: James Stewart
ISBN: 9781285740621

This textbook survival guide was created for the textbook: Calculus, edition: 8. The full step-by-step solution to problem: 17 from chapter: 1 was answered by , our top Calculus solution expert on 11/10/17, 05:27PM. Calculus was written by and is associated to the ISBN: 9781285740621. This full solution covers the following key subjects: divisible, Integer, Positive, prove. This expansive textbook survival guide covers 16 chapters, and 250 solutions. Since the solution to 17 from 1 chapter was answered, more than 252 students have viewed the full step-by-step answer. The answer to “Prove that if n is a positive integer, then 7n 2 1 is divisible by 6.” is broken down into a number of easy to follow steps, and 16 words.

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Prove that if n is a positive integer, then 7n 2 1 is