Problem # 1: The objective is to solve the following nonlinear equation using th

Question

Problem # 1: The objective is to solve the following nonlinear equation using the Newton Raphson algorithm. Pick your own initial guess and iterate until the mismatch is les than 10. f(x) -3 Where: f(x)1.5cos(x) +10sin(x) robli # 2: to sohlowing twoar The objective is to solve the following two nonlinear equations using the Newton Raphson algorithm: f,(x,x21.5 6(X,,X2)=-0.5 Where: f(x,,x2)-x2-1.1x, cos(%) +11x, sin(%) f2(xi,x,) = 9.9x2-1.1x2 sin(%)-11x2 cos(%) Find the Jacobian Matrix Letx(o)=0,x2)=1,use the Newton Raphson algorithm to a find a solutions,, x2 such that max-1.5-f, (x,, X 1. 2. -0.5-f, (xi, x 10-5

Explanation / Answer

PLEASE ENTER THE FOLLOWING COMMAND IN THE MATLAB M FILE AND THAN RUN IT

clc

clear all

x=input('please enter the intial guesss');            %TAKES THE intial guess input from the user.

n=0; %n denotes the iteration

fn=0;                                                             %this is functions intial value

dfn=0; % dfn shows differentiation of function

tol=10e-5;    %tolerance

for n=1:1000                                               % iteration number looping

fn=3+(10*sin(x))-(1.5*cos(x));    %function

  

dfn=(10*cos(x))+(1.5*sin(x));

x=x-fn/dfn;                                               %newton raphson iteration formula

if abs(fn/dfn)<tol %checks the condition when mismatch is less than 10e-5

fprintf('the final value of x is %d and this took iteration %d .',x,n);

return;

end

end

RESULT

please enter the intial guesss     0.666

the final value of x is -1.523252e-01 and this took iteration 4 .

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