=for timestamp
Do Dez  2 18:37:29 CET 2004

=head3 27. Hausaufgabe

=head4 Buch Seite 56, Aufgabe 1

Kennzeichne das Verhalten der Funktion M<f: x \mapsto f(x)> für immer größer
werdende M<x>-Werte!

Skizziere den Graphen!

=over

=item a)

M<f(x) = -\frac{4}{1 + x}; D_f = \mathds{R}_0^+;>

M<\left|-\frac{4}{1+x_s}\right| E<lt> \varepsilon; \Rightarrow
-\frac{4}{\varepsilon} - 1 E<lt> x_s;>

=item b)

M<f(x) = \frac{3}{x^2}; D_f = \mathds{R}^+;>

M<\left|\frac{3}{x^2}\right| E<lt> \varepsilon; \Rightarrow x_s E<gt>
\sqrt{\frac{3}{\varepsilon}};>

=back

=helper MyBook::Helper::Gnuplot

# File automatically generated by Plot.pm

# Global settings
set samples 10000
unset border
set xtics axis
set ytics axis
set xzeroaxis lt -1
set yzeroaxis lt -1

# Coordinate system settings
set title ""
set xlabel "\nx\n"
set ylabel "y\n"
set xrange [ -10.000000 : 10.000000 ]
set yrange [ -10.000000 : 10.000000 ]
set grid
set xtics 5.000000
set ytics 5.000000

# Function definitions
func0(x) = -4./(1.+x)
func1(x) = 3./x**2

# Plotting
plot func0(x) t "f1" w l lt 1, func1(x) t "f2" w l lt 2

=hend