Question

photo of the code please and an explnation if possible,

Construct a simple MATLAB function program my_factorial which calculates product of first n positive integer numbers (i.e. find factorial n!). For full points: - Make sure you protect the code from illogical use (n must be positive integer) - Test the function by comparing with built in MATLAB function factorial(n) - Make sure you test your function for any limitations. O marks) -3. Using my factorial function from the previous subtask, construct new MATLAB function program my_sin which evaluates et using Maclaurin expansion: x3 x5 x x x2k+1 sin(x) = x - + + + ... += x + (-1)* (2k + 1)! 4 . K The number of terms in this expansion needs to be provided by the user of the function as an positive integer value and value of x must be a single numeric value and not an array on matrix. Examine numerical limitations of this function and comment on their origin. 15 marks) 1.4. Write a main MATLAB program in which subtask by comparing with numerical error (numerror = my sin - matlab_sin) and the number of terms in your my_sin functio the semilogy() command more useful than scale. For full points: - Test your code for any limitations and comment - If you discovered some limitations, makes AB program in which you test the my sin function from the previous Tunction sin(x). Create a variable that represents our my_sin function and the effect of x-axis you are using. You may mg 12 -- matlab_sin) and then examine the effect of more useful than plot(). This displays the y-axis on a logarithmic (25 marks) mations and comment on their origin ations, make sure you protect the code from them.

Answer 1

%2

function f = my_factorial(n)
if isnumeric(n) && length(n)==1 && n>=0 && (n==floor(n))%if n is a positive scalar integer
f=1;
for i=1:n
f=f*i;
end
else%else, we throw an errror
error('n must be a positive integer!!!')
end

con IIIIIIII function f = my_factorial (n) if isnumeric (n) && length (n)==1 && n>=0 && (n==floor (n)) if n is a positive scalar integer f=1; for i=1:n f=f*i; end elsešelse, we throw an errror error('n must be a positive integer!!!') end

%3

function sx = my_sin(x,n)
if ~(isscalar(x) && isnumeric(x))%checking if x is a scalar value
error('x must be a scalar numeric value!!!')
elseif ~(isscalar(n) && isnumeric(n) && n>0 && floor(n)==n)%checking n
error('n must be a positive integer!!!')
else
sx=0;
for k=0:n-1
sx=sx+(-1)^k*x^(2*k+1)/(my_factorial(2*k+1));
end
%sx=sx+x;
end

N TILL III | 009 function sx = my_sin(x, n) if (isscalar (x) && isnumeric(x)) $checking if x is a scalar value error('x must be a scalar numeric value!!!') elseif (isscalar (n) && isnumeric(n) && n>0 && floor (n) ==n) checking n error('n must be a positive integer!!!!) else sx=0; for k=0:n-1 sx=3x+ (-1)^k*x* (2*k+1)/(my_factorial (2*k+1)); end sx=sx+x; end

%4

clear
clc
x=pi/4;%checking at x = pi/4;
n=1:6;%value of n
er=zeros(1,length(n));
for i=1:length(n)
sinx=my_sin(x,n(i));
er(i)=abs(sinx-sin(x));%storing absolute error
end
semilogy(n,er,'-*')
xlabel('number of terms')
ylabel(' log of error')
grid on
title('my\_sin vs matlab\_sin')

IIIIIIIIIIIIII clear clc x-pi/4; $checking at x = pi/4; n=1:6; $value of n er-zeros (1, length (n)); for i=1:length (n) sinx=my_sin(x, n(i)); er(i)=abs(sinx-sin(x)); storing absolute error end semilogy (n, er,'-*') xlabel('number of terms') ylabel(' log of error') grid on title('my\_sin vs matlab\_sin')

my_sin vs matlab_sin log of error 10-12 1 1.5 2 2.5 4.5 5 5.5 6 3 3.5 4 number of terms