MATLAB Let f(x)=cosx. define a 1 =a, a 2 = f (a), a 3 = f(a2) = f (f(a)),..., a

Question

MATLAB
Let f(x)=cosx. define a1 =a, a2 = f (a), a3 = f(a2) = f (f(a)),..., a n+1 =f(an ). plot the first 5 terms of this sequence (which, since it converges to a fixed point of f). Find the limit to within .00001. Gnerate the sequence using a for loop and test the five decimal place accuracy with an if statement (i.e., is | a n+1 - an | < .00001?) Alternatively, use a while loop plz shows code MATLAB
Let f(x)=cosx. define a1 =a, a2 = f (a), a3 = f(a2) = f (f(a)),..., a n+1 =f(an ). plot the first 5 terms of this sequence (which, since it converges to a fixed point of f). Find the limit to within .00001. Gnerate the sequence using a for loop and test the five decimal place accuracy with an if statement (i.e., is | a n+1 - an | < .00001?) Alternatively, use a while loop plz shows code

Explanation / Answer

part 1:

clc

a=1;

x=a;

for i=1:5

F(i)=cos(x);

x=F(i);

end

stem(F)

2)

clc

a=67;

x=a;

F(1,1)=cos(x);

F(1,2)=cos(F(1,1));

diff=abs(F(1,i)-F(1,i+1));

i=2;

while diff>=10^(-5)

i=i+1;

F(1,i)=cos(x);

x=F(i);

diff=abs(F(1,i)-F(1,i-1));

  

end

stem(F)

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