Consider the following equation: log(10)x = e(-x) a) Demonstrate that the given equation has only one root at the interval [1,2]. b) Calculate a value approximation of that root, applying 4 iterations of the Bissection Method, beginning at the initial interval a₁ = 1, bo = 2. Build a table with the necessary values of k, ak, bk, xk, f (xk), signals of f(), to k = 0,1,2,3. c) Give an error estimative to the root approximation obtained in (b). d) Indicate how many interations are necessary to get a root approximation with error less than 10(-³).
Consider the following equation: log(10)x = e(-x) a) Demonstrate that the given equation has only one root at the interval [1,2]. b) Calculate a value approximation of that root, applying 4 iterations of the Bissection Method, beginning at the initial interval a₁ = 1, bo = 2. Build a table with the necessary values of k, ak, bk, xk, f (xk), signals of f(), to k = 0,1,2,3. c) Give an error estimative to the root approximation obtained in (b). d) Indicate how many interations are necessary to get a root approximation with error less than 10(-³).
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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![Consider the following equation:
log(10)x = e(-x)
a) Demonstrate that the given equation has only one root at the interval [1,2].
b) Calculate a value approximation of that root, applying 4 iterations of the
Bissection Method, beginning at the initial interval a = 1, bo = 2. Build a table
with the necessary values of k, ak, bk, xk, f (xk), signals of f(), to k = 0,1,2,3.
c) Give an error estimative to the root approximation obtained in (b).
d) Indicate how many interations are necessary to get a root approximation with
error less than 10(-³).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff1e1b415-86bd-4a44-8122-cfbfb1e8f6ee%2Fed3302c5-b9c8-43ae-9122-e4d8d602350f%2Fs2nnza9_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the following equation:
log(10)x = e(-x)
a) Demonstrate that the given equation has only one root at the interval [1,2].
b) Calculate a value approximation of that root, applying 4 iterations of the
Bissection Method, beginning at the initial interval a = 1, bo = 2. Build a table
with the necessary values of k, ak, bk, xk, f (xk), signals of f(), to k = 0,1,2,3.
c) Give an error estimative to the root approximation obtained in (b).
d) Indicate how many interations are necessary to get a root approximation with
error less than 10(-³).
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