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Direction field analysis Consider the general first-order

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett ISBN: 9780321570567 2

Solution for problem 61AE Chapter 7.8

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Calculus: Early Transcendentals | 1st Edition

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Problem 61AE

Direction field analysis Consider the general first-order initial value problem \(y^{\prime}(t)=a y+b\), \(y(0)=y_{0}\), for \(t \geq 0\), where a, b, and v0 are real numbers.

a. Explain why y = -b/a is an equilibrium solution and corresponds to a horizontal line in the direction field.

b. Draw a representative direction field in the case that a > 0. Show that if \(y_{0}>-b / a\), then the solution increases for \(t \geq 0\), and if \(y_{0}<-b / a\), then the solution decreases for \(t \geq 0\).

c. Draw a representative direction field in the case that a > 0. Show that if \(y_{0}>-b / a\), then the solution decreases for \(t \geq 0\), and if \(y_{0}<-b / a\), then the solution increases for \(t \geq 0\).

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Leslie Ogu PSYC 2012 03/02/2016 ­ Group Processes Pt. 1 Characteristics of Groups ➢ 2 or more people ➢ Interactions are interdependent and influence each other ➢ Help basic human needs to belong, get information, establish our identity, and social norms ➢ Members tend to be similar to one another ○ This is usually due to the group one belongs to having an impact on who you are if you spend enough time with them ○ Adapting to the culture Deindividuation ➢ Why do people behave differently in crowds ➢ Def:​ the loosening of normal constraints on behavior when in a crowd, leading to an increase in impulsive and deviant acts ○ When we are around large numbers of people, we tend to get a little crazier because we are less wary of the consequences (since the group is so large) ➢ When people become deindividuated, normal constraints against deviant behavior is lessened ○ Feel less accountable for actions (more excuses) ○ ** Deindividuation does not require face­to­face contact ** ■ Ex: internet, social media ➢ Factors affecting deindividuation ○ Group Size ■ The larger the group, the more deindividuated people become ● they feel less accountable because it’s harder to single one person out ○ Anonymity ■ The more anonym

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Chapter 7.8, Problem 61AE is Solved
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Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

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Direction field analysis Consider the general first-order