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Let and Find: (a) AB. (b) A2 = AA. (c) B2 = BB.

Fundamentals of Differential Equations | 8th Edition | ISBN: 9780321747730 | Authors: R. Kent Nagle, Edward B. Saff, Arthur David Snider ISBN: 9780321747730 43

Solution for problem 3E Chapter 9.3

Fundamentals of Differential Equations | 8th Edition

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Fundamentals of Differential Equations | 8th Edition | ISBN: 9780321747730 | Authors: R. Kent Nagle, Edward B. Saff, Arthur David Snider

Fundamentals of Differential Equations | 8th Edition

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Problem 3E

Let and Find: (a) AB. (b) A2 = AA. (c) B2 = BB.

Step-by-Step Solution:
Step 1 of 3

Devan Atteberry 4/8/2016 Chem 312 Week #2: Functional Groups and Resonance Functional Groups Carboxylic acid Random, carbon double bonded to oxygen, oxygen, hydrogen (COOH) - Tends to be acidic Ester Random, carbon double bonded to oxygen, oxygen, carbon (COOC) - Common in natural compounds - Can be fragrant Ketone carbon double bonded to oxygen, carbon Aldehyde Random, carbon double bonded to oxygen, hydrogen Amide Random, carbon double bonded to oxygen, nitrogen Alcohol Carbon, oxygen, and hydrogen Amine Carbon, nitrogen - Can have more than one carbon as long as it isn’t double bonded to oxygen - Tends to be basic (proton acceptor) Alkene carbon double bonded to carbon Alkyne carbon triple bonded to carbon Alkane carbon single bonded to other carbons Strengths of Acids - Values of pKa less than zero indicate a strong acid - Oxygen will always have a charge if bonded to more than two elements - When oxygen only has two bonds it is neutral - In an equilibrium reaction you go from stronger acid to lesser acid o Favor the products  Keq greater than 1  Product less acidic than reactants Rationalizing Acid Base Trends (1) Inductive Effect - chlorine is more electronegative than carbon which induces a dipole thus making the OH bond weaker and less polar which increases the acidity - resonance (2) Hyrbridization - Sp3 < Sp2< Sp more acidic (3) H-bonding (intramolecular) Resonance - Multiple ways to represent exact same molecule, but not exactly precise - General trends of resonance o (1) lone pair next to a pi bond o (2) pi bond next to pi bond o (3) Empty P-orbital next to pi bond o (4) Empty P-orbital next to lonepair - Only really be considered about resonance when lone pair is involved - Trigonal parametal = 3 bonds plus a lone pair - There is no need to worry about resonance when there are Pi bonds connected to the element in question

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Chapter 9.3, Problem 3E is Solved
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Textbook: Fundamentals of Differential Equations
Edition: 8
Author: R. Kent Nagle, Edward B. Saff, Arthur David Snider
ISBN: 9780321747730

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Let and Find: (a) AB. (b) A2 = AA. (c) B2 = BB.