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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 ao = 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 ao = 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).

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter6: Exponential And Logarithmic Functions
Section6.1: Exponential Functions
Problem 60SE: The formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is...
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C & D only.

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).
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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