: Find a root of f(x) = 3x + sin(x) - e* ? Fig. 5 shows the (x) 3x + sin(x) - e*. It's clear from the graph that there are two roots, one lies between 0 and 0.5 and the other between 1.5 and 2.0. Then the bisection iterations are given by: Iteration 1st 2nd Consider the function f(x) in the interval [0, 0.5] since f (0) xf (0.5) is less than zero. 3rd 4th 5th 6th XI Table 2: Xr Xm 0.5 0.25 0.25 0.5 0.393 0.25 0.393 0.34 0.34 0.393 0.367 0.34 0.367 0.354 0.354 0.367 0.3605 f(xm) + 0 1+1+1 0.5 Fig. 5 Ea
: Find a root of f(x) = 3x + sin(x) - e* ? Fig. 5 shows the (x) 3x + sin(x) - e*. It's clear from the graph that there are two roots, one lies between 0 and 0.5 and the other between 1.5 and 2.0. Then the bisection iterations are given by: Iteration 1st 2nd Consider the function f(x) in the interval [0, 0.5] since f (0) xf (0.5) is less than zero. 3rd 4th 5th 6th XI Table 2: Xr Xm 0.5 0.25 0.25 0.5 0.393 0.25 0.393 0.34 0.34 0.393 0.367 0.34 0.367 0.354 0.354 0.367 0.3605 f(xm) + 0 1+1+1 0.5 Fig. 5 Ea
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 54E
Related questions
Question
![: Find a root of f(x) = 3x + sin(x) - e* ?
Fig. 5 shows the (x) = 3x + sin(x) - e*.
It's clear from the graph that there are two roots, one lies
between 0 and 0.5 and the other between 1.5 and 2.0.
Then the bisection iterations are given by:
Iteration
1st
2nd
3rd
Consider the function f(x) in the interval [0, 0.5] since f (0) xf (0.5) is less than zero.
4th
5th
6th
Table 2:
XI
Xr
Xm
0
0.5
0.25
0.25
0.5
0.393
0.25 0.393
0.34
0.34
0.393 0.367
0.34
0.367
0.354
0.354 0.367 0.3605
f(x)
+
0
1+1+1
0.5
Fig. 5
Ea](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe53d6781-4b71-4186-b8d0-d81b070ecd80%2Fedf11496-786a-406b-83a3-636872b8b90e%2Ft1ib1n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:: Find a root of f(x) = 3x + sin(x) - e* ?
Fig. 5 shows the (x) = 3x + sin(x) - e*.
It's clear from the graph that there are two roots, one lies
between 0 and 0.5 and the other between 1.5 and 2.0.
Then the bisection iterations are given by:
Iteration
1st
2nd
3rd
Consider the function f(x) in the interval [0, 0.5] since f (0) xf (0.5) is less than zero.
4th
5th
6th
Table 2:
XI
Xr
Xm
0
0.5
0.25
0.25
0.5
0.393
0.25 0.393
0.34
0.34
0.393 0.367
0.34
0.367
0.354
0.354 0.367 0.3605
f(x)
+
0
1+1+1
0.5
Fig. 5
Ea
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