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Practice Exercises T 13-19. Finding roots with Newton's method For the given function f and initial approximation o, use Newton's method to approximate a root of f. Stop calculating approximations when two successive approximations agree to five digits to the right of the decimal point after rounding. Show your work by making a table similar to that in Example 1 13. f(x) = x² – 10; xo 14. f(x) = x³ + x² + 1; x = −1.5 15. f(x) = sin x + x = 1; x = 0.5 16. f(x) = e + x − 5; xo = 1.6 17. f(x) = tan x 2x; xo 18. f(x) = x ln (x + 1) − 1; xo = 1.7 19. f(x) = cos ¹x - x; x = 0.75 = = 1.2 = 3

Practice Exercises T 13-19. Finding roots with Newton's method For the given function f and initial approximation o, use Newton's method to approximate a root of f. Stop calculating approximations when two successive approximations agree to five digits to the right of the decimal point after rounding. Show your work by making a table similar to that in Example 1 13. f(x) = x² – 10; xo 14. f(x) = x³ + x² + 1; x = −1.5 15. f(x) = sin x + x = 1; x = 0.5 16. f(x) = e + x − 5; xo = 1.6 17. f(x) = tan x 2x; xo 18. f(x) = x ln (x + 1) − 1; xo = 1.7 19. f(x) = cos ¹x - x; x = 0.75 = = 1.2 = 3

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question 13 and 15. Show work, thank you! Answers are given.
Practice Exercises T 13-19. Finding roots with Newton's method For the given function f and initial approximation o, use Newton's method to approximate a root of f. Stop calculating approximations when two successive approximations agree to five digits to the right of the decimal point after rounding. Show your work by making a table similar to that in Example 1 13. f(x) = x² – 10; x = 3 14. f(x) = x³ + x² + 1; x = −1.5 15. f(x) = sin x + x − 1; x = 0.5 16. f(x) = e + x − 5; xo = = 1.6 17. f(x) = tan x - 2x; x = 1.2 18. f(x) = x ln (x + 1) - 1; x = 1.7 19. f(x) = cos ¹x = x; x = 0.75 -
Transcribed Image Text:Practice Exercises T 13-19. Finding roots with Newton's method For the given function f and initial approximation o, use Newton's method to approximate a root of f. Stop calculating approximations when two successive approximations agree to five digits to the right of the decimal point after rounding. Show your work by making a table similar to that in Example 1 13. f(x) = x² – 10; x = 3 14. f(x) = x³ + x² + 1; x = −1.5 15. f(x) = sin x + x − 1; x = 0.5 16. f(x) = e + x − 5; xo = = 1.6 17. f(x) = tan x - 2x; x = 1.2 18. f(x) = x ln (x + 1) - 1; x = 1.7 19. f(x) = cos ¹x = x; x = 0.75 -
13. n 0 3 r≈ 3.16228 15. n 0 1 2 3 T≈ 0.51097 e in 0.5 0.51096 0.51097 0.51097 Xn 3 3.1667 3.16228 X n 3.16228
Transcribed Image Text:13. n 0 3 r≈ 3.16228 15. n 0 1 2 3 T≈ 0.51097 e in 0.5 0.51096 0.51097 0.51097 Xn 3 3.1667 3.16228 X n 3.16228
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