%% Annotated Matlab transcript -- 2/1
%% CS 323 - Doug DeCarlo

% LOS example from last time: the value can actually be zero...
x = 0:1e13:1e16;
plot(x,x.*(sqrt(x+1)-sqrt(x)),'g',x,x./(sqrt(x+1)+sqrt(x)),'b');

% another LOS example: computing exp(-5) via taylor series:

% Looking at terms in its taylor series
n = 0:20;
(-5).^n ./ factorial(n)
plot(n,(-5).^n ./ factorial(n))

% And when we add them up and plot the result up to term n:
for n = 1:20
x = 0:n;
a(n) = sum((-5).^x ./ factorial(x));
end
plot(1:20,a)


%% Function noise - example from book

x = linspace(0.99998, 1.00002, 100);
f1 = (x-1).^3;
f2 = x.^3 -3*x.^2 + 3*x - 1;
f3 = -1 + x .* (3 + x .*(-3 + x));

plot(x,f1,'r',x,f2,'g',x,f3,'b',x,0)