Question

Using Matlab

**1. Give the flowchart for finding the root of the
function f(x) = [tanh(x-2)] [sin(x+3)+2]**

**with the following methods (6 significant figures
required):**

**a) Modified Regula Falsi (Choose two reasonable integers
as your initial upper and lower bounds)**

**b) Newton’s Method (Choose one reasonable integer as
your initial guess for the root)**

Answer #1

% Newton

f=@(x) tanh(x-2).*(sin(x+3)+2);

deriv_f=@(x) tanh(x-2).*(cos(x+3))+
(sech(x-2))^2.*(sin(x+3)+2);

x=1;

for i=1:10

x=x-f(x)/deriv_f(x);

end

disp('Newton Solution is : ')

disp(x)

% Regula -falsi modified

a=2.1;

b=1.91;

if (f(a)*f(b)<0)

c=b-(f(b)*(b-a))/(f(b)-f(a));

for i=1:20

if(f(b)*f(c)<0)

a=b;

b=c;

c=b-(f(b)*(b-a))/(f(b)-f(a));

else

b=c;

c=b-(f(b)*(b-a))/(f(b)-f(a));

end

end

else

disp('Error ')

end

disp('Regular Falsi Method:')

disp(c)

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