Part 2 In this section, we wll try to quantify the error in calculating values o

Question

Part 2 In this section, we wll try to quantify the error in calculating values of functions which are error prone due to the limits of machine precision. Let us revisit the example we encountered in class. 1, Plot the function g(r) = log(1+1) for different ranges of z. After you have explored the function behavior for different ranges of z, focus on the values of z 0" What happens if you decrease z to magnitudes comparable to machine epsilon? 2. Write down the Taylor expansion for this function to 5th order (one more term added to the series in class) while explicitly showing your calcula tions. Use the LaTeX functionality of the markdown cells in Jupyter to show your caleulations. Don't skip steps. I want to see the details of your calculations. 3. Compare the two versions of g(z) - the Taylor expansion and the actual function n some detail. When is the expansion valid? When is it not

Explanation / Answer

This seems a Maths question wrongly placed in Computer Science. Though I have knowledge to answer the Question.
1. g(x) = log(1+x)/x where x -> 0. here at x->0 equation is in 0/0 form.
so, by applying L Hospital rule:
d( log(1+x) )/d(x) = 1/(1+x)) = 1/(1 + 0) = 1.

Sorry, but I can only answer first quesition acording to rules of Chegg.

Thanks,
Hrudwik

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