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Exercise "LaTeX"

First, install LaTeX on your system:

Debian based systems: install Tex Live distribution with the command

sudo apt-get install texlive texlive-latex-extra texlive-font-utils

MacOS with HomeBrew: install MacTeX distribution. It seems that you first need to install "homebrew cask" and then
```
brew cask install mactex
```
or
```
brew cask install basictex # allegedly a small but functional version of MacTeX
```

Now, the exercises:

(Mandatory) Consider the following "quick-and-dirty" implementation of the exponential function (which only uses multiplications and divisions),
```
static double ex(double x){
if(x<0)return 1/ex(-x);
if(x>1.0/8)return Pow(ex(x/2),2); // explain this
return 1+x*(1+x/2*(1+x/3*(1+x/4*(1+x/5*(1+x/6*(1+x/7*(1+x/8*(1+x/9*(1+x/10)))))))));
}
```
Make a one-/two- page report, in LaTeX, about this implementation along the following lines: i) introduce the exponential function; ii) explain why this implementation might actually work; iii) test whether it works in practice. There should be plots in your report.
(Optional)
1. Is there any numerical advantage in using this convoluted expression for the Taylor series,
```
1+x*(1+x/2*(1+x/3*(1+x/4*(1+x/5*(1+x/6*(1+x/7*(1+x/8*(1+x/9*(1+x/10)))))))));
```
  instead of the ordinary
```
1+x+x²/2!+x³/3!+x⁴/4!+...
```
  ?
2. Is there any numerical advantage in inverting the sign of the argument for negative arguments?
(Optional) Make a complex version of this implementation,
```
static complex cex(complex z){
...
}
```
and check whether it works or not.