Question

Show that the bisection method can be used to obtain the zeros of $f(x) = \sqrt{x} - cos(x)$ in [0, 1]. Find the number of iterations necessary to find the solution accurate up to five decimal places. a) Implement the bisection method in MATLAB to approximate the zeros of $f(x)$. Accept $f(x)$ as an anonymous function using @(x), the initial interval $[a_0, b_0]$, and a bound for the error to produce an approximation. b) Use the bisection method to find $\sqrt{5}$ accurate to within $10^{-6}$.

          Show that the bisection method can be used to obtain the zeros of $f(x) = \sqrt{x} - cos(x)$ in
[0, 1]. Find the number of iterations necessary to find the solution accurate up to five decimal
places.
a) Implement the bisection method in MATLAB to approximate the zeros of $f(x)$. Accept
$f(x)$ as an anonymous function using @(x), the initial interval $[a_0, b_0]$, and a bound for
the error to produce an approximation.
b) Use the bisection method to find $\sqrt{5}$ accurate to within $10^{-6}$.

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show that the bisection method can be used to obtain the zeros of fx sqrtx cosx in 0 1 find the number of iterations necessary to find the solution accurate up to five decimal places a imple 25206

Added by Josefina B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

12/19/2023

Step 1

Step 1: To show that the bisection method can be used to obtain the zeros of $f(x) = \sqrt{x} - cos(x)$ in [0, 1], we need to verify that the function satisfies the conditions of the bisection method. Show more…

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Show that the bisection method can be used to obtain the zeros of $f(x) = \sqrt{x} - cos(x)$ in [0, 1]. Find the number of iterations necessary to find the solution accurate up to five decimal places. a) Implement the bisection method in MATLAB to approximate the zeros of $f(x)$. Accept $f(x)$ as an anonymous function using @(x), the initial interval $[a_0, b_0]$, and a bound for the error to produce an approximation. b) Use the bisection method to find $\sqrt{5}$ accurate to within $10^{-6}$.

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Transcript

00:01 So we need to consider here that is x square minus 3 which is equal to 0.

00:05 Now that is we need to find a value of f point 1 .6 that is 1 .6 whole square minus of 3.

00:15 That is we have to write minus of 0 .44 which is less than 2 .0.

00:21 And now we have we need to find value of f at 1 .8 which is 1 .8 whole square minus of 3.

00:30 That is equal to 0 .24 which is greater than 2 .0.

00:35 So therefore roots lie between 1 .6 to 1 .8.

00:42 So we need to apply here the first iteration that is x1 is equal to by by 1 .8 by 2 which is equal to 1 .7.

00:55 So from here we need to write fx1 is equal to 1 .7 whole square minus 3.

01:06 That is equal to minus of 0 .11 less than 2 .0.

01:11 And as you and we know that at f point 8 is greater than 2 .0.

01:17 So therefore now we need to write that is x2 is equal to 1 .7 plus 1 .8 by 2.

01:27 So which is equal to 1 .75.

01:31 So fx2 is equal to we have here that is 0 .625 which is greater than 2 .0.

01:42 And we know that fx1 is less than 2 .0.

01:49 Now fx3 is equal to we have here x1 plus x2 whole upon 2 which is equal to 1 .725.

02:00 And then fx3 we have to write then that is minus of 0 .024375 which is less than 2 .0.

02:13 And we have to write now that is fx2 is greater than 2 .0...

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