PROBLEMS

Question 20.1

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Question 20.2

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

Question 20.3

u5RNecwPszyN+loBgnRYfzNQVvkGDMQ914voGrENIqZrX4sfBbY7fXwvcD42cONoKSPmQtM0IvYS5Ge1QdIXkB3UyCesgaKNTnIZxlVS3syyn2bGiATwiz2q3naJcLvNKiqOgUiW1nl4hxIKBg0KwGHwF9wIeksQ7g2GhUzlhEv6+yQb3cfXoAYC9e1sKJLtnhhV/FXoejRMQSblx0vty1WzkvDuRp1wtteJDKrplWoQM5P6Ye28Wn1QHXTbkd+XkV5LZbqvtTNbxUWet/8vKO7210J2OJliRww8qAqp8s2qAUqb8DQDvPzfKpbnJrJxnuBT4tnz6WUcJ4cag7bwuSp0DU9CsQHtluvO757E2Ocm4AR7eSGXsCOWyuobRPnD+S2igNmaWVOu0jzJiSWusUMXjWJFLUDMXtgUfv3vG3mBv3Pei4c7HpT0XIFsmGRYYh+ect5ezJO3rCbe

Question 20.4

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

Question 20.5

c++wAyer57RJJ9vk9XdzgKXuT45oZ1mBRZbf10wJ0PzaYtgWKny8pXwd3A+1P4JVoRcrz0BP3JkIPA3SF8R6HTh1K8Ezqh+860DmeRtKSJj25RGP66sd/neSXJN7Sbyrp55TKC5u8I7u/ZAHQw9SPNDEvzakaUJq

Question 20.6

hfMOSZ9hCw3bLAGB7asbfm7fzDw7mYCUpzTIREpx8oS+TyetBNXBgMLkX0EPZO9ckgaM4eB64bfIa6bq2x2wdymV151xJr/KuPA69XrsfPTTTbFUd5SAR6Um8O1D65XP0wUFKZmcjBxDbgxVPvux8cyrvMdCer/mluXvUifBQ1b3XsyWsSlJxbeECfrDVYemPZ/lurNVNVovmws4lNghc9C1ZYJsEvdGB6NHgujqLFyTt4xq2Edi/W2i6ocLD+KVAT0LfShhtB+tNl+IBkUu92UjmwrcFbGMpn+FX19gVk7WYadsruiqLlG6QLo/viVDLYc2tX0WabeHxR2d

Question 20.7

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

Question 20.8

ryRI9TxzSsFB/3n6ZnbvP08DYLYBjDbcgUz6jyWVxjSGB5OIDVevVKFrssn1l1f9MpVoRLqWKghxwqm08RT+ZR5dsw9j//e2hoEN2zaVhEmBn1LmJR0gy1PFTC8UCJS3tBVQh7zsZcYcQydMVrE/OdAeTi9FkEfyxM9Fucs9gL6YNuunIZPDPhfEP0vv5mPmm4ZK5laSCjTrMFbU6spV8/dQuY7eI4X7l75vII1deNYcqMVebY1sKg0DnOqypf1skz6WULHEV6kyidKrtb+UII2R83wuLTfCMEdOJPfcpAHcj0oD/2OxfUftZ14cyCzOs89uw1B4pmJLOji3

Question 20.9

E6ksGW/Fq+4jTPXRKNfE4D2+rgC8tARaj3IOjCFsNzS7hLNhNmUJINyNd/3pzZY+R47VMBX309E9xCeljR3oV7t7lL+WPkWXLOhqD/kCer9rWuDl8Sxj+VEJzfpSnT6InfNhRfJnayliVaw3RGepHp7N/8ADh2KUg2/Yp/JopOV8B/NbZ25qyl6BX6U7jyIiXbXuptDfAajZIO+R1e+3Z0CO7nXeEXG1uYyz6ClJhsKOPHApoiCjrx1E3yWIDqsBMD4yuEheDjdPAAxdi3k71y21MvjM48uBYyPxyOaNlFaNNFo7OUso0g==

Question 20.10

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

Question 20.11

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

Question 20.12

nT06a17PVvUBgh4IlG0A1O4+T7kc2CW8SNHsWexWslYOVvF47bL4ez3jgU6yiIe8iBWdp5NGDFscxg7knp7zeK2ZuAw6NELloLidWTN6xk9b8wCle4Wt7jsNfchkH2cQjxirkIAleLUdDIK6LaCKCMRvBSw=

Question 20.13

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

Question 20.14

CT8vr5w7tdPy2dk6p3a1pEtyNfWcYtCT1V2GJmlQd4KWI+Ke/wVvRCYznTcPeX4Z92+Dgezh/EcBMRqfEFKpfG6esKFs71eS65jN7TmTKA77UdpnpT9T8rEIt+6TFKa+zdQM/2nU7xMMd76vXKC6/PQuWZNlGDdcRa/egq2cS12XeJd3JAi98+4JJUuiQ953iqMhOY+/y8YaM87T/I5BpCg96wlS1YM2Mk8lDUNSgtK6hFp3Q2ueNUqYx1s=

Chapter Integration Problems

Question 20.15

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

Question 20.16

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

Question 20.17

j2r0iqpCoyTH4Z/BOQgdi47MTQYjXPmMQcoxu2n/gpCvSZns2gVOSqEceTpMl7XgTtqyAzxu8CgZwGUfER3vIgvdCM4D0dqLbzmxxrMd/7zJC/p2LQC7bCWsh40iiqKG10wm49kuUo+CaTPLolYBb+2tQOc3QDUFkNbKX2X2N4lRZitEsoobz8oEcgKJIeYNOFZRaHgLTT4WJzBW

Question 20.18

34kqz15Oq76tlZByhcAkrqmC9amDkv+C6BBaCBxysTiuINuyxr/Vymkj/Pq2m55sImkPSCg66MbFg+r9YdrKhqcASMtX1tnvigpUa9DsmsE4789ZsZNMiM4GQZrlbb9MgJUH/leV/I/b54EwaMqzueV69wUnWtxbyhcZbQgXB/k=

Challenge Problems

Question 20.19

kkccBnyR9teRqg6g/L9rRmyllVZXo2sYoq+rotk9TmW+qgo6suLEF2xMFmLnCwKOpteeQ1ptDMqJKBz8vY31Cw74LRr8gS63wvXr6tu3NPomz2Q6J8H8hEkI1SV/WuhcHjjIwlEzscPVg1MDuKuURmfgAKXGw28+gdznOg5qWOYe2q8MtdTchp0x3TcpXK85iJ0GHV1Vqzo5m1/C7Xeb89kzpLr+sIw1MyRdjk8IfiSyRjKC0Jcob5EjqLpYo4HFfDGETHAtcN5QnTHwKoufLK8Yyubxn0NsPzKfz+e1tbywam8eu7011mtck2XJ90fBXbC7tpxk1SaE5zrhmLqxjDsxs/hArwm+bKldBUU5mMxkAollmwGOzD4QtQ4FDQbT

Question 20.20

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

382

Selected Readings for this chapter can be found online at www.whfreeman.com/tymoczko3e.