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Solved: 2328. Approximations with Taylor polynomials a.

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

Solution for problem 23 Chapter 9.1

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 23

2328. Approximations with Taylor polynomials a. Use the given Taylor polynomial p2 to approximate the given quantity. b. Compute the absolute error in the approximation assuming the exact value is given by a calculator. Approximate 11.05 using f 1x2 = 11 + x and p21x2 = 1 + x>2 - x2>8.

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Copyright ©: Hannah Kennedy, Kent State University 1 2/24/16 Lecture notes: Normative ethics 1. Normative Ethics review a. Normative ethics = ethical theory i. Theories of right action: the content of morality (2 things we look for) 1. Systems of determining when actions are right/wrong, good/bad (3 things) a. Intention (motivation) b. Consequences (outcome) c. Action itself 2. Systems that make clear what actions are morally relevant ii. Determining whether there are universal moral principles 1. If there are universal moral principles, can they be subordinated and prioritized 2. Theories we will discuss a. Moral realism b. Deontology i. Natural law theory = we are moral (virtuous) to the extent that we fulfill (meet) our human nature 1. Foot ii. Rule based 1. But these rules can be different based on a number of variables c. Consequentialism d. Virtue ethics i. Foot 3. Phillipa Foot: October 3 1920 – October 3 2010 a. Wanted to modernize virtue ethics, Aristotelian by training b. Grover Cleveland’s granddaughter and captain in British army c. Philosophy i. Ethics 1. Virtue ethicist with natural law theory mixed in ii. Metaphysics 1. Naturalist (soft realism) iii. Epistemology 1. Empiricist d. (Intrinsic) natural goodness = is present in living things only and depends on a relationship between an individual and the life form of its species (characteristics that help us survive and reproduce) i. life form = these are things necessary for maintenance and reproduction 1. first maintenance 2. then reproduction a. Given example from text: i. A deer’s swiftness is a natural goodness e. (Instrumental) second goodness = characteristics that make a thing useful to another thing (don’t have to be living things) f. Aristotelian categorical = a categorical statement that relates two classes or things i. Categorical statements = those that relate 2 categories or classes of things 1. Given example from text (Aristotelian categorical): a. “rabbits are herbivores” Copyright ©: Hannah Kennedy, Kent State University 2 i. Must be a statement that relates a species with a characteristic that allows that species to survive and reproduce ii. Considered a norm 1. Norm = standards, often generally accepted as true ii. Syllogist logic depends on terms: 1. All m are p 2. All s are m 3. All s are p g. How to determine if a living thing has natural goodness i. Establish an Aristotelian categorical 1. Have a characteristic that’s important to the life cycle a. These must be teleological i. Telos = goal/purpose/end b. Ex = rabbits are herbivores ii. Statement about the particular animal (living thing) that I am assessing a. Ex = Bugs Bunny is an herbivore i. Therefore he has natural goodness h. Qualifiers to Natural Goodness (2 things) i. Aristotelian Categoricals, which establish our natural goodnesses, are only applicable to natural habitat ii. Having natural goodnesses does not guarantee survival 1. Having natural goodness only suits us (prepares us) to survive i. We can translate this framework to people (human beings) i. What’s essential (what’s our telos) to humans (2 things) 1. Rationality a. Animals are sub­rational 2. Our society ii. Our categoricals will be related to virtues that help the society function 1. Can translate from physical needs to societal needs a. Difficulties with the transition i. Complexity of our goals ii. Complexity of our rational capacity iii. Establishing basic statements is hard iv. Have to accept that being social is part of our nature and that we cannot survive on our own 4. Essay Activity a. What makes us “human”—possible characteristics: i. Ability to interact ii. Rationality iii. Auto­didactic (be able to self­teach) iv. Faith v. Capacity for language vi. Social vii. Relationship 1. A literal connection to other living things viii. Commitment to morality ix. Capacity for emotion x. Empathize Copyright ©: Hannah Kennedy, Kent State University 3 1. Fellow­feeling xi. Awareness of action 1. Potentially regarding the awareness of consequences xii. Autonomy 1. Self­directed xiii. Introspection xiv. Capacity for pain 1. Often physical (sentience) b. Can you pick just one or do there need to be more than 1 i. If you can pick more than one then how do you value actions c. Look at list, pick, and think about how it affects the second question Copyright ©: Hannah Kennedy, Kent State University 1 1. Essay: due Monday of week 9 a. No quoting, no sources, all our ideas b. 500­750 words 2. Normative ethics = ethical theory = theories of right action; concerned with the content of morality a. Content of morality i. What things/characteristics make actions right/wrong (moral), good/bad 1. Are the boundaries between right and wrong stable (Clear cut) a. i.e. a lot of gray area ii. What subject matters are worthy of moral consideration 1. i.e. is liking coffee a moral subject matter iii. Consider whether or not we can have ultimate moral principles (universal) b. What makes an action moral i. Intention = motive behind the action ii. Consequences = outcome of the action 1. i.e. Mill was a consequentialist iii. Action itself = how I perform the action c. Is there an ultimate moral principle or not (answer will often be yes or no) 3. General Moral Theories Moral theory Based on… Philosopher(s) Other info Moral realism Morality Plato Deontological Intention based Kant ­ these are rules and rights based ­ the only thing that matters is that I intended to follow the rule (motive) Consequentialism Consequences Mill, Smart ­ the consequence of an (utilitarians) action carries moral worth Virtue ethics Good character Aristotle, Foot ­ places worth in intention, action, and outcome

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Chapter 9.1, Problem 23 is Solved
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Textbook: Calculus: Early Transcendentals
Edition: 2
Author: William L. Briggs
ISBN: 9780321947345

Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321947345. The answer to “2328. Approximations with Taylor polynomials a. Use the given Taylor polynomial p2 to approximate the given quantity. b. Compute the absolute error in the approximation assuming the exact value is given by a calculator. Approximate 11.05 using f 1x2 = 11 + x and p21x2 = 1 + x>2 - x2>8.” is broken down into a number of easy to follow steps, and 51 words. Since the solution to 23 from 9.1 chapter was answered, more than 240 students have viewed the full step-by-step answer. This full solution covers the following key subjects: . This expansive textbook survival guide covers 128 chapters, and 9720 solutions. The full step-by-step solution to problem: 23 from chapter: 9.1 was answered by , our top Calculus solution expert on 12/23/17, 04:24PM. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 2.

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Solved: 2328. Approximations with Taylor polynomials a.