Question

I only need help on doing number 4

LON-CAPA COurse ConSSOE-First ear-SprirASSGT9 (1)pd softEdge elackboard Conter 4d Metro Boomin No mpstate/Downloads/ASSGT9%20(1) pdf Users/april/AppData/Local/Pac Your task: Design, code, and debug a MATLAB script that: (1) Asks the user (use a nenu) what kind of function (m-file or anonymous function) will be used. If an m-file, have the user enter the filename; if an anonymous function, have the user enter the function (hint: use MATLAB's eval function in your script to appropriately assign these tasks to desired variables) C) Calls a user-defined function (ie, m-file) that requests the user to enter the domain of interest (i.e., the start and end point of the plot), and produces an annotated plot (ie, a plot with appropriate labels) of the mathematical function in the desired domain. Use MATLAB'sfd a command G) Displays a ne au asking the user what type of analysis they wish to perform; choices are finding the mathematical function's zeros, minima, maxima, or area under the curve Uses a s wit ch case structure (with the nenu response as its expression) to: (a) Call a user-defined function that finds as many zeros as the user desires and displays (b) Call a user-defined function that finds as many minima as the user desires and (4) the location of each zero to the screen. Use MATLAB'sfer o command displays the location of each minimum to the screen. Use MATLAB's f Ii nbnd command (c) Call a user-defined function that finds as many maxima as the user desires and displays the location of each maximum to the screen. Use MATLAB's f imnbnd command. Note that you need to use the negated function for this step, make sure that you ask for this function in step 1 d) Within the main script, find the area under the curve between two points entered by the user. Give the user the option of using either the trapz or quad methods (5) Allow the user to select as many functional analyses as they desire (i.e., return to step 3) (6) Allow the user to run the program as many times as they desire (i.e, return to step 1)

Answer 1

The solution to question 4 along with required details in comments are given as follows:

----------------------- MAIN SCRIPT FILE

clear all
clc
f=@(x) sin(x); % a sample function

want_to_continue=1;

while (want_to_continue)
% Menu used for switch satements
fprintf('\n\nPlease enter one among the following choices to select the operation to be performed:');
fprintf('\n1. Find muliple zeros');
fprintf('\n2. Find multiple maxima');
fprintf('\n3. Find multiple minima');
fprintf('\n4. Find Area under curve');
fprintf('\n5. Want to exit?');
  
num=input('\nEnter the choice:');
  
switch(num)
case 1 % find N zeros
N=input('\nFind the number of zeros to be found:');
roots=find_multiple_zeros(f,N); % call the function
g=sprintf('%3.5f ',roots); % display the statement
fprintf('The Roots of the function are obtained obtained at :%s\n',g);
case 2 % find N minimas
N=input('\nFind the number of minima(s) to be found:');
roots=find_multiple_minima(f,N); % call the function
g=sprintf('%3.5f ',roots); % display the results
fprintf('The minima of the function are obtained at :%s\n',g);
case 3 % find N maximas
N=input('\nFind the number of maxima(s) to be found:');
roots=find_multiple_maxima(f,N); % call the function
g=sprintf('%3.5f ',roots); % display the results
fprintf('The maxima of the function are obtained at :%s\n',g);
case 4
N1=input('\n Enter the first limit:'); % find the lower limit of the curve
N2=input('\n Enter the second limit:'); % find the upper limit of the curve
M=input('\n Enter 1 for trapz method and 2 for quad method:'); % select the method
area=find_aoc(f,N1,N2,M); % call the function
fprintf('The area of the function between %d and % d is %3.5f sq. units.\n',N1,N2,area);
case 5
want_to_continue=0;
otherwise
fprintf('Wrong Choice entered!')
end
end

-------------------------- FUNCTION 1: FIND MULTIPLE ZEROS

function roots=find_multiple_zeros(f,N)
% find N zeros of the function
starting_points=linspace(0,N*pi,100); % divide the interval betweeen 0 and N*pi into 100 pieces
for i=1:1:100
% Look for the zeros in the function's current interval.
x(i)=fzero(f, starting_points(i));
end
x_unique=x(diff(x)>1e-12); % identify unique zeros

roots=x_unique; % return unique zeros

end

------------------------ FUNCTION 2: FIND MULTIPLE MINIMAS

function roots=find_multiple_minima(f,N)
starting_points=linspace(0,2*(N+1)*pi,(N+1)); %divide the interval betweeen 0 and 2*(N+1)*pi into (N+1) pieces
for i=1:1:N
% Look for the minima in the function's suninterval.
x(i)=fminbnd(f,starting_points(i),starting_points(i+1));
end
x_unique=x;

roots=x_unique; % return the minimas

end

-------------------------- FUNCTION 3: FIND MULTIPLE MAXIMA

function roots=find_multiple_maxima(f,N)
starting_points=linspace(0,10*(N+1)*pi,10*(N+1));
h=@(x)-f(x); % negate the function to convert to maxima problem
for i=1:1:N
% Look for the zeros in the function's current subintervals
x(i)=fminbnd(h,starting_points(i),starting_points(i+1));
end
x_unique=x;

roots=x_unique(1:N); % return the maximas

end

----------------------------------- FUNCTION 4: FIND AREA UNDER CURVE

function area=find_aoc(f,N1,N2,M)
x=linspace(N1,N2,1000)';
h=@(x) abs(f(x));
% remove the sign from the function so that all y values are positive. This is to
% ensure that area obatined is always positive

if M==1 % if method selected is one, use trapezoidal method
area = trapz(x,h(x));
  
elseif M==2 % if method selected is two, use quad method
area= quad(h,N1,N2);
else
area=0; % othewise, return 0
end
end

--------------------------- SCREENSHOTS OF CODES

main script.m X find multiple zeros.m X find multiple mínima.m find-multiple maxima.m X find-aoc.m X + lear al1 clc f-C(x) sin (x) a sample function want to continue-1 while (want to continue) % Menu used for switch 3atements fprintf (n\nPlease enter one among the following choices to select the operation to be performed:); fprintf'nl. Find muliple zeros') fprintf ("n2. Find multiple maxima') fprintf(n3. Find multiple minima') fprintf (n4 Find Area under curve) fprintf ('n5. Want to exit? 10 12 13 14 15 num-input ("nEnter the choice:) 17 18 switch (num) case 1 20 N-input (nFind the number of zeros to be found: roots-find multiple zeros (f, N) 21 call the function sprintf ( " %3. 5f ' , roots) ; fprintf( 'The Roots of the function are % display the statement 23 24 - 25 26 27 28 obtained obtained at : %s\n",g); case 2 find N mínimas N-input ('nFind the number of minima (s) to be found:) roots-find multiple minima (f, N) g sprintf ( ' %3 fprintf('The minima of the function are obtained at 3\n",g); call the function . 5f , roots) ; display the results case3 % find N maximas 30 N-input (nFind the number of maxima (s) to be found:'

30 31 32- N=input ('\nFind the number of maxima (s) to be found :"); roots-find multiple_maxima (f,N) g sprintf ( , %3 . 5f , roots) ; fprintf (The maxima of the function are obtained at : %s\n",g); call the function display the results 34- 35- 36- 37 38- 39 40- 41 42 43 case4 N1-input ('n Enter the first limit:' N2=input ('\n Enter the second limit:'); M=input ('\n Enter 1 f r trapz method and 2 for quad method :'); 唐 select the method area-find aoc ( f , N1 , N2 , M); fprintf ('The area of the function between 휨d and d is %3.5f sq. units.\n',n1,N2 , area); find the lower limit of the curve % find the upper limit of the curve % call the functio case 5 want to continue ; otherwise fprintf ('Wrong Choice entered!) end end 46

main-script.m find-multiple zeros.m × find-multiple minima.m X find multiple maxima.m X find-a oc.m + function roots-tind multiplezeros (f,N) % find N zeros f the function starting points-linspace (0, N*pi, 100): - asvide the sncerva beceen o ana p ne 00 N*pi into 4 中for i-1 : 1 : 100 一 Look for the zeros in the function ,s current interval. x(i)-fzero(f, starting_points (i)); end x unique=x (diff (x)>1e-12); identify unique zeros roots=x unique; return unique zeros 12-end

main script.m X find_multiple_zeros.m Xfind_multiple_minima.m find multiple_ maxima.m find_aoc.m+ function roots=find multiple minima (f,N) 2 ו 3tarting_points=linspace (0,2* (N+1) *pi, (N+1)); for i-1:1:N into (3+1) pieces %divide the interval betwee en 0 and 2*(N+1)*pi - Look for the minima in the function 's suninterval. X (1) =fmanbnd (f, startingpoints (1) , startingpoints (1+1) ) ; - - 6end | x-unique=x; roots=x unique ; return the minimas 10 end 12

main script.m × find-multiple-zeros.m X find multiple minima.m 1 甲function roots-find multiple maxima (f,N) 2starting point 3h- (x) -f (x) 4- 부for i=1 : 1 :N X find multiple maxima.m X find-aoc.m X + s-linspace (0,10 (N+1) *pi, 10* (N+1)) % negate the function to convert to maxima pr blem Look for the zeros in the function s current subintervals x(İ)-frinbnd (h , startingpoints (i, startingpoints (1+1) ) ; - - 7-end uniquex: 10 roots=x unique (1 :N); % return the maxima s 12end

main-script.m ×| find-multiple zeros.m XI find-multiple minima.m find-multiple-maxima.m 지 find-aoc.m X function area-find aoc (f, N1, N2, M) | x=linspace (N1,N2, 1000)" ; h- (x) abs (f (x)) % remove the sign from the function 30 that all y values are positive. This is to % ensure that area obatined is always positive % if method selected is one , use trapezoidal method area trapz (x, h (x) ) ; 10 - elseif M==2 % if method selected is two, use quad method area- quad (h, N1, N2) 12 else area-O othewise, return 0 14 - 15 - end end

-------------------------------------- SAMPLE OUTPUT

Command Window Please enter one among the following choices to select the operation to be performed: 1. Find muliple zeros 2. Find multiple maxima 3. Find multiple minima 4. Find Area under curve 5. Want to exit? Enter the choice:1 Find the number of zeros to be found:4 The Roots of the function are obtained obtained at :0.00000 3.14159 6.28319 9.42478 Please enter one among the following choices to select the operation to be performed: 1. Find muliple zeros 2. Find multiple maxima 3. Find multiple minima 4. Find Area under curve 5. Want to exit? Enter the choice:2 Find the number of minima (s) to be found:!5 The minima of the function are obtained at 4.71240 10.99557 17.27876 23.56194 36.12831 Please enter one among the following choices to select the operation to be performed: 乓1. Find muliple zeros

Command Window 2. Find multiple maxima 3. Find multiple minima 4. Find Area under curve 5. Want to exit? Enter the choice:3 Find the number of maxima () to be found:5 The maxima of the function are obtained at 1.57080 6.38963 7.85398 12.77931 14.13716 Please enter one among the following choices to select the operation to be performed: 1. F1nd muliple zeros 2. Find multiple maxima 3. Find multiple minima 4. Find Area under curve 5. Want to exit? Enter the choice:4 Enter the first limit:1 Enter the second limit:2 Enter 1 for trapz method and 2 for quad method: 1 The area of the function between 1 and 2 is 0.95645 sq. units. Please enter one among the following choices to select the operation to be performed: 1. Find muliple zeros

2. Find multiple maxima 3. Find multiple minima 4. Find Area under curve 5. Want to exit? Enter the choice:4 Enter the first limit:1 Enter the second limit:2 Enter 1 for trapz method and 2 for quad method: 2 The area of the function between 1 and 2 is 0.95645 sq units. Please enter one among the following choices to select the operation to be performed: 1. Find muliple zeros 2. Find multiple maxima 3. Find multiple minima 4. Find Area under curve 5. Want to exit? Enter the choice:5