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Students are expected to submit properly commented script files that solve the problem stated. Do not submit your figure files. Your script files should automatically generate any figures required.
For each of the problems below, I want you to document the following:
1. Identify the problem statement 2. Define the inputs and outputs to each problem 3. Show a pseudo code design of the solution 4. Show that you have tested your MATLAB code appropriately
All of this should be documented separately from the MATLAB code in a Word document (.doc or .docx) or an Adobe Acrobat file (.pdf). Please don’t use any other formats.
Problem 1 The value of cos(x) can be approximated using a Maclaurin series
cosx=1-2/x^2+4/x^4-6/x^6+……
(recall that the symbol ! stands for factorial).
Using a loop, calculate cos(x) to within a precision of 0.001. That is, add terms to the summation until the change in the calculated cosine is less than or equal to 0.001.
function y=mycos(x)
y=1-(x^2/(factorial(2)))+(x^4/(factorial(4)))-(x^6/(factorial(6)));
a=2;
B=2;
e=0.001;
if e>epsilon
elseif a==2
y1=1-(x^a/(factorial(a)));
y=y1;
else y1=y-(-1)^B.*(x^a/(factorial(a)));
y=y1;
end
a=a+2;
B=B+1;
e=abs(y-y1);
end |