Question

6. Construct Anonymous Functions to compute the functions below. Use the AFs within a program to find Flx) in the range x (0:0.1.3]. Print the results as a table with columns x, and F(o) f(x)=x3-x-2 for 0 f(x) = x3 _ x _ 1 for 1 1 x 2 f(x) =x3 _ χ for 2.5 x < 3 Construct the anonymous function f(x,y) as shown for the mathematical function below. This function will be used in the future in a program to computes f(x,y) for values of x=[1,10] in steps of 0.5; and for values of y = x2. 7. 10-3ex F(x,y) = sin(y)2

IN MATLAB

Answer 1

Please find below the required MATLAB code. I have added comments at suitable places to explain the details. Further, I also plotted the two functions with respect to x values on x-axis to give an understnading of how function f are behaving with two definations.

Note that Q 6. has been solved through part 1 of the code and Q7 through part 2.

Please find below the selectable MATLAB code:

----------------------------------------------------------MAINFILE.M

clear all
clc

%% PART 1
x=[0:0.1:3];

% call function to compute function 1
for k=1:length(x)
result(k,:)=compute_f(x(k));
end
% display result table
fprintf('Result Table 1:\n')   
disp(result)
% plot (x,f(x)) result to see how f(x) changes over x
plot(result(:,1),result(:,2),'r-')
title('Figure 1 using Anonymus Function 1')
clear x result

%% PART 2
% Calling Function 2
x=[1:0.5:10];
% call function to compute function 1
for k=1:length(x)
y=x(k)^2;
result(k,:)=compute_F2(x(k),y);
end
% display result table
fprintf('Result Table 2:\n')
disp(result)
% plot (x,f(x)) result to see how f(x) changes over x
figure
plot(result(:,1),result(:,2))
title('Figure 2 using Anonymus Function 2')

-------------------------------------------------- Function for computing QUESTION 6

function result=compute_f(x)
% Function for part 1

if x>=0 & x<1
f=x^3-x-2; % this f(x) will be used if 0<=x<1
elseif x>=1 & x<2
f=x^3-x-1; % this f(x) will be used if 1<=x<2
elseif x>=2 & x<=3
f=x^3-x; % this f(x) will be used if 2<=x<3
end

result=[x f]; % save result in two columns in form of (x,f(x))
end

-------------------------------------------------FUNCTION FOR QUESTION 7

function result=compute_F2(x,y)
% Function for part 2

F=(10^(-3)*exp(x))/(sin(y^2)); % Function defination

result=[x F]; % save result in two columns in form of (x,f(x))
end

-------------------------------------------

Note that bothe has been called from the mainfile.m.

------------------------------------- SCREENSHOT OF THE CODES

plotfunct.m compute f.mcompute_F2.m+ clear all clc %% PART 1 x-[0:0.1:31: % call function to compute function 1 | for k=1 : length (x) result (k, : )=compute-f (x (k) ) ; 12 13 14 15 16 end % display result table fprintf ('Result Table 1:\n) disp (result) % plot (x,f(x)) result to see how f(x) changes over x esult (:,2), '-') plot (result(,1),r title( Figure 1 using Anonymus Function 1') clear x result 18 19 20 21 %% PART 2 Calling Function 2 x I1:0.5: 101: % call function to compute function 1 for k1length (x) 23 24 25 26- 27 28 29 30 y=x (k) ^2; result (k, :) compute F2 (x (k) , Y) end display result table fprintf ('Result Table 2:\n) disp (result) plot (x,f(x)) result to 3ee how f(x) changes over x

plotfunct.m X| compute-f.m compute-F2.m function result-computef(x) 1 - Function for part 1 f=x"3-x-2; % this f(x) will be used if 0<=x<1 f=x^ 3-x-1; thì 3 f (x) will be used if 1<=x<2 8-1 elseif X>=2 & x<=3 f=x^3-x; % this f (x) will be used if 2<=x<3 10- end result-[x f]; % save result in two columns in form f (x,f(x)) 13 - 14 15 end

plotfunct.mx compute fmcompute F2m+ 早function result-compute-F2(x,y) % Function for part 2 F-(10^ (-3) *exp (x)) / (sin (y^2) ) ; % Function defination result=[x F]; % save result in two columns in form of 4-1 (x,f(x)) 7end

----------------------------------------------SAMPLE OUTPUT OF CODE

Command Window Result Table 1 0 2.0000 0.10002.0990 0.20002.1920 0.3000-2.2730 0.4000 -2.3360 0.50002.3750 0.60002.3840 0.7000-2.3570 0.8000 -2.2880 0.90002.1710 1.00001.0000 1.1000 -0.7690 1.2000 -0.4720 1.3000 0.1030 0.3440 0.8750 1.4960 2.2130 3.0320 3.9590 6. 0000 7.1610 8.4480 9.8670 2.4000 11.4240 2.5000 13.1250 2.6000 14.9760 1.4000 1.5000 1.6000 1.7000 1.8000 1.9000 2.0000 2.1000 2.2000 2.3000

Command Window 2.6000 14.9760 2.7000 16.9830 2.8000 19.1520 2.9000 21.4890 3.0000 24.0000 Result Table 2: 1.0000 0.0032 1.5000 -0.0048 2.0000 0.0257 0.0124 3.0000 0.0319 3.5000 -0.0494 4.0000 -0.0546 0.0903 0.8432 5.5000 -0.3231 0.4052 1.1170 1.4954 7.5000 -3.9252 8.0000 5.0130 8.5000-5.1547 8.2963 9.5000 15.0897 10.000072.0727 2.5000 4·5000 5.0000 6.0000 6.5000 7.0000 9.0000

-------------------------------------------PLOT OF TWO FUNCTIONS For visual understanding of output

Figure 1 using Anonymus Function 1 25 20 15 10H 5ト -5 0.5 1.5 2.5

Figure 2 using Anonymus Function 2 20 10 0 10 20 -30 -50 -60 70 -80 10