I would like to know how to answer this question, it has to be done all in MATLA
ID: 3847931 • Letter: I
Question
I would like to know how to answer this question, it has to be done all in MATLAB and I'm new to it so I am having a hard time figuring out how it's done.
(a) Write a function using for or while loop that computes an approximation to natural logarithm
function loge(1 + x) using the above formula. Your function must take x and n as function
input arguments. n is the number of terms you want to keep in your approximation. The
approximation will get more accurate if you keep more terms.
(b) Re-write your function using vectorization techniques.
(c) Determine the minimum number of terms you need to approximate loge(0.5) = -0.69314718 to
eight decimal digits? Print out your result on the screen as follows:
"It takes n=1000 terms to approximate log(0.5) = -0.69314718 to six digits, the approximation
is -0.693147179453401."
(d) Compute the error in the approximation to log(0.5) = -0.69314718 using n = 1, 5, 10, 25, 50, 100, 1000
terms in the above formula. Print a nice table of the results as follows:
Explanation / Answer
(a)
create a file mylog.m and paste below code in it:
function [s] = mylog(x,n)
s = 0;
i = 1;
for i = 1:n
term = ((-1)^(i+1))*(x^i)/i;
s = s + term;
end
end
Sample Run:
(c)
Matlab code:
format long;
actual = -0.69314718;
i = 2;
while(abs(actual - mylog(-0.5,i)) >= 10^-8)
i = i + 1;
end
out = mylog(-0.5,i);
i
fprintf('It takes n = %d terms to approximate log(0.5) = -0.69314718 to eight digits and the approximation is ',i);
out
Sample Output:
(d)
Matlab code:
format long;
actual = -0.69314718;
n = [1, 5, 10, 25, 50, 100, 1000];
for i = 1:size(n,2)
out = mylog(-0.5,n(i));
error = abs(actual - out);
fprintf('%d %d %d ',n(i),out,error);
end
Sample Output:
(b)
function [s] = mylog(x,n)
format long;
syms k
s = symsum( ((-1)^(k+1))*(x^k)/k , k, 1, n);
end