# Exercici 06.6

kill(all)$

f(x):= exp(1/x) ;
g(x):= exp(1/x) /( exp(1/x) - 1);

'limit(f(x), x, 0, minus) = limit(f(x), x, 0, minus) ;

'limit(f(x), x, 0, plus) = limit(f(x), x, 0, plus) ;

'limit(f(x)/x, x, 0, minus) = limit(f(x)/x, x, 0, minus) ;

'limit(f(x)/x, x, 0, plus) = limit(f(x)/x, x, 0, plus) ;

'limit(g(x), x, 0, minus) = limit(g(x), x, 0, minus) ;

'limit(g(x), x, 0, plus) = limit(g(x), x, 0, plus) ;

'limit(x*g(x), x, 0, minus) = limit(x*g(x), x, 0, minus) ;

'limit(x*g(x), x, 0, plus) = limit(x*g(x), x, 0, plus) ;

wxplot2d([g(x)], [x,-3, 3], [gnuplot_preamble, "set grid;"])$

wxplot2d([x*g(x)], [x,-3, 3], [y, -2, 8] , [gnuplot_preamble, "set grid;"])$