Question
Please use Matlab to solve and comment
i·m, "y be output in Macia ing fprintf to consolidate. NOTE: The midterm exam will include material covered in this homework Find the point of intersection of the following two equations x)-8sinl Do this a) Using the bisection method using initial guesses of O and 4n b) Using the Newton-Raphson method using initial guesses of O the secant method using initial guesses of 0 and Using the false-position method using initial guesses of 0 and 4n For a)-d), itera for each part te until you have at least 3 sign ) The number of iterations needed to converge on the intersection. i) Make a plot showing where each guess was (4 plos total, I per method) e) Why did some methods converge faster than others for this exa ter than others for this example
Explanation / Answer
a)using bisection method
f=@(x)-5*x.^2-2;
a=0;
b=12.57142;
for i=1:100
c=(a+b)/2;
if f(c)>0
b=c;
else
a=c;
end
end
fprintf('Approxinmation Root is %f',c);
b) using newton raphson method:
f=@ 8* sin(x.^2-2)
df=@(x)-5*x.^2-2
a=0;b=0;
x=a;
for i=1:1:100
x1=x-(f(x)/df(x));
x=x1;
end
sol=x;
fprintf('Approximate Root is %f',sol)