Write code to approximate3 Squareroot 25 by applying the a b

Write code to approximate^3 Squareroot 25 by applying the a) bisection method and b) false position methods to the equation x^3 - 25 = 0. Do not use bisect.p or falsepos.p; code the algorithms on your own and submit to Cody. You choose the starting guesses-these will be the Cody input. Determine the result accurate to at least to 5 sig figs.

Solution

On the work space

%Bisection method

clear;

f=input(\'enter a function of x\')

x0=input(\'enter x0\')

x1=input(\'enter x1\')

x=0;

if f(x0)*f(x1)>0

error (\'choose another nterval\')

else

while abs(f(x))>0.00001

x=(x0+x1)/2

if f(x0)*f(x)>0

x0=x;

else x1=x;

end

end

end

On command window

>> krishna
enter a function of x@(x)x.^3-25

f =

    @(x)x.^3-25

enter x02

x0 =

     2

enter x13

x1 =

     3

x =

    2.5000

x =

    2.7500

x =

    2.8750

x =

    2.9375

x =

    2.9063

x =

    2.9219

x =

    2.9297

x =

    2.9258

x =

    2.9238

x =

    2.9248

x =

    2.9243

x =

    2.9241

x =

    2.9240

x =

    2.9240

x =

    2.9240

x =

    2.9240

x =

    2.9240

x =

    2.9240

x =

    2.9240

x =

    2.9240

>>

Falsi method:

On work space

%Regula falsi method

clear;

f=input(\'enter a function of x\')

x0=input(\'enter x0\')

x1=input(\'enter x1\')

x=0;

if f(x0)*f(x1)>0

error (\'choose another nterval\')

else

while abs(f(x))>0.00001

x=(x0*f(x1)-x1*f(x0))/(f(x1)-f(x0))

if f(x0)*f(x)>0

x0=x;

else x1=x;

end

end

end

On command window

>> jj
enter a function of x@(x)x.^3-25

f =

    @(x)x.^3-25

enter x02

x0 =

     2

enter x13

x1 =

     3

x =

    2.8947

x =

    2.9233

x =

    2.9240

x =

    2.9240

x =

    2.9240

>>