hw2 done up to ex3

hw2/assignment2.m

@@ -0,0 +1,36 @@
+%% Assignment 2
+% Name: Claudio Maggioni
+%
+% Date: 19/3/2019
+%
+% This is a template file for the first assignment to get started with running
+% and publishing code in Matlab.  Each problem has its own section (delineated
+% by |%%|) and can be run in isolation by clicking into the particular section
+% and pressing |Ctrl| + |Enter| (evaluate current section).
+%
+% To generate a pdf for submission in your current directory, use the following
+% three lines of code at the command window:
+%
+%  >> options.format = 'pdf'; options.outputDir = pwd; publish('assignment2.m', options)
+%
+
+%% Problem 3
+
+syms x;
+
+f = exp(x);
+df = diff(f);
+x_0 = 1;
+err = zeros(10, 1);
+h = zeros(10, 1);
+
+for i = 1:10
+    h(i) = 10^(-i);
+    err(i) = abs(subs(df,x,x_0) - my_diff(f, x, x_0, h(i)));
+end
+
+loglog(h, err)
+
+function approx = my_diff(f, x, x_0, h)
+    approx = (subs(f,x,x_0 + h) - subs(f, x, x_0)) / h;
+end

hw2/hw2.tex

@@ -56,4 +56,11 @@ $$
 
 \subsection*{Point e}
 Division and multiplication may suffer from cancellation.
+
+\section*{Exercise 3}
+\subsection*{Point d}
+The error at first keeps getting exponentially smaller due to a better approximation of $h$ when computing the derivative
+(i.e. $h$ is exponentially nearer to 0), but at $10^{-9}$ this trend almost becomes the opposite due to loss of significant
+digits when subtracting from $e^{x+h}$ $e^x$ and amplifiying this error by effectively multiplying that with exponentially
+increasing powers of 10.
 \end{document}