Question

Comprehension Check 1. Write commands to solve the equation e <x+2 by graphing functions and determining points of intersection. Putting it All Together Create a new section in your Live Script for this portion. Include all commands, output and graphs you use. Add explanations as needed. Consider the function below (after giving it your name and filling in the month and day of the month of your birth). -YOUR-NAME-(x) 《cos (.5#x)-exp《co s (x-Day)))/sqrt(Month-x^2) - Use Matlab to do each of the following 1. Estimate the y-intercept to 9 decimal places. 2. Estimate the x-intercepts to 9 decimal places. 3. Write the domain in interval notation. 4. Write the range in interval notation, accurate to 4 decimal places. 5. Solve the inequality YOUR NAME (x)> sin(x). Write your answer in interval notation, accurate to 4 decimal places

Answer 1

clc;
clear all;
YOUR_NAME = @(x) (cos(.5*x)-exp(cos(x-Day)))./sqrt(Month-x.^2);
fprintf('The y-intercept = %0.9f\n',YOUR_NAME(0));
a = -1;b = 1;
u=YOUR_NAME(a);
v=YOUR_NAME(b);
err=abs(b-a);
while (err>10^-9)
x0=b-v*(b-a)/(v-u);
a=b;
u=v;
b=x0;
v=YOUR_NAME(b);
err=abs(b-a);
end
fprintf('The x-intercept = %0.9f\n',b);
x = -2:0.00001:2;
f = YOUR_NAME(x);
I = imag(f) == 0;
Xl = min(x(I));
Xr = max(x(I));
fprintf('The domain is [%0.4f %0.4f]\n',Xl,Xr);
Alhasn_min = min(YOUR_NAME(x(I)));
Alhasn_max = max(YOUR_NAME(x(I)));
fprintf('The range of the function in the selected domain [%0.4f %0.4f]\n',Alhasn_min,Alhasn_max);
Fun = @(x) YOUR_NAME(x)-sin(x);
a = -1;b = 1;
u=Fun(a);
v=Fun(b);
err=abs(b-a);
while (err>10^-5)
x0=b-v*(b-a)/(v-u);
a=b;
u=v;
b=x0;
v=Fun(b);
err=abs(b-a);
end
if(Fun(-sqrt(2)) > 0)
fprintf('Alhasn_(x)> sin(x) is true for x in [%0.4f %0.4f]\n',-sqrt(2),b);
elseif(Fun(sqrt(2)) > 0)
fprintf('Alhasn_(x)> sin(x) is true for x in [%0.4f %0.4f]\n',b,sqrt(2));
end

OUTPUT

The y-intercept = 0.376313459
The x-intercept = 0.783889597
The domain is [-1.4142 1.4142]
The range of the function in the selected domain [-292.4427 92.2908]
YOUR_NAME_(x)> sin(x) is true for x in [-1.4142 0.2966]