ch3sols - Math 343 - Homework Assignment 8 - Due Nov. 1 1....

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Math 343 - Homework Assignment 8 - Due Nov. 1 1. Page 119: 1(b)(d), 2(b)(d), 3(c), 4(c), 13, 15(c)(d), 19, 1-2(b) f ! x " ! 1 " x , x 0 ! 0, x 1 ! 0.6, x 2 ! 0.9. y 0 ! f ! 0 " ! 1, f ! 0.6 " ! 1. 264911, f ! 0.9 " ! 1. 378405 P 1 ! x " ! x ! ! ! " " 1. 264911 x ! 0.4415183 x " 1.0 P 2 ! x " ! ! x ! "! x ! " ! ! "! ! " " 1. 264911 x ! x ! " ! ! 0.3 " " 1. 378405 x ! x ! " ! " ! 1. 851852 ! x ! "! x ! " ! 7. 027283 x ! x ! " " 5. 105204 x ! x ! " ! ! 0.070227 x 2 " 0.4836543 x " P 1 ! 0.45 " ! 1. 198683, P 2 ! " ! 1. 203424 The true error ! 1.45 ! P 1 ! " ! 5. 476208 # 10 ! 3 The true error ! ! P 2 ! " ! 7. 358329 # 10 ! 4 f ! x " ! ! 1 " x " 1/2 , f $ ! x " ! 1 2 ! 1 " x " ! 1/2 , f $$ ! x " ! ! 1 4 ! 1 " x " ! 3/2 , f $$$ ! x " ! 3 8 ! 1 " x " ! 5/2 | f $$ ! x " | ! 1 4 ! 1 " ! " 3 " 1 4 for all x in # 0,1 $ . f $$$ ! x " ! 3 8 1 ! 1 " x " 5/2 " 3 8 for all x in # $ . R 1 ! x " ! f $$ ! ! " 2! x ! x ! " ! ! 1 8 ! 1 " ! " 3 x ! x ! " , where ! is between 0 and 0.6. | R 1 ! " | ! f $$ ! ! " 1 2 |0.45 ! ! " | " 1 4 1 2 ! "! 0.15 " ! 0.0084375 R 2 ! x " ! f $$$ ! ! " 3! x ! x ! "! x ! " ! 1 3! 3 8 ! 1 " x " ! 5/2 x ! x ! "! x ! " , where ! is between 0 and 0.9. | R 2 ! " | ! f $$ ! ! " 1 3! ! ! "! ! " | " 3 8 1 6 ! "! "! " ! 1. 898438 # 10 ! 3 1-2(c) f ! x " ! tan ! x " , x 0 ! 0, x 1 ! x 2 ! y 0 ! f ! 0 " ! 0, f ! " ! 0.6841368, f ! " ! 1. 260158 P 1 ! x " ! ! 0 " x ! ! ! " " 0.6841368 x ! 1. 140228 x P 2 ! x " ! ! 0 " ! x ! "! x ! " ! ! "! ! " " x ! x ! " ! ! " " 1. 260158 x ! x ! " ! " ! ! 3. 80076 x ! x ! " " 4. 667252 x ! x ! " ! 0.866492 x 2 " 0.6203328 x P 1 ! " ! 0.5131026, P 2 ! " ! 0.4546144 The true error ! |tan ! " ! P 1 ! " | ! 3. 004753 # 10 ! 2 The true error ! |tan ! " ! P 2 ! " | ! 2. 844067 # 10 ! 2 f $ ! x " ! sec 2 ! x " , f $$ ! x " ! 2sec 2 ! x " tan ! x " , f $$$ ! x " ! 2 ! 2 ! x " tan 2 ! x " " sec 4 ! x "" 1
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0 2 4 6 8 10 0.2 0.4 0.6 0.8 1 x y ! f $$ ! x " 10 20 30 40 50 0 0.2 0.4 0.6 0.8 1 x y ! f $$$ ! x " f $$ ! x " " f $$ ! 1 " ! 2sec 2 ! 1 " tan ! 1 " ! 10. 66986 % 11 f $$$ ! x " " f $$$ ! 1 " ! 2 ! 2 ! 1 " tan 2 ! 1 " " sec 4 ! 1 "" ! 56. 70300 % 57 R 1 ! x " ! f $$ ! ! " 2! x ! x ! 0.6 " ! sec 2 ! ! " tan ! ! " x ! x ! " , where ! is between 0 and 0.6. | R 1 ! 0.45 " | ! f $$ ! ! " 1 2 |0.45 ! ! " | " 11 1 2 ! "! 0.15 " ! 0.37125 R 2 ! x " ! f $$$ ! ! " 3! x ! x ! "! x ! 0.9 " ! 1 3 ! 2 ! ! " tan 2 ! ! " " sec 4 ! ! x ! x ! "! x ! " , where ! is between 0 and 0.9. | R 2 ! " | ! f $$ ! ! " 1 3!
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This note was uploaded on 10/30/2011 for the course MATH 151a taught by Professor Staff during the Fall '08 term at UCLA.

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ch3sols - Math 343 - Homework Assignment 8 - Due Nov. 1 1....

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