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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
100%
Question 13 and 15. Show work, thank you! Answers are given.
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
-
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
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
