# Exercici 08.6

## Apartat a)

kill(all)$

f(x):=(x + sin(x)) / (x - sin(x));

f1(x):=x + sin(x)$     diff(f1(x), x);
f2(x):=x - sin(x)$      diff(f2(x), x);

g(x):= (cos(x)+1) / (1-cos(x));
limit(g(x), x, inf);

g1(x):=f1(x)/x;     g2(x):=f2(x)/x;

limit(g1(x)/g2(x), x, inf);

limit(f(x), x, inf);

## Apartat b)

kill(all)$

f(x):= (sin(x)) / (x^2*sin(1/x)) ;

limit(f(x), x, 0);

f1(x):=sin(x)$               diff(f1(x), x);
f2(x):=x^2*sin(1/x)$     diff(f2(x), x);

g(x):= (cos(x)) / (2*sin(1/x)*x-cos(1/x));

limit(g(x), x, 0);

g1(x):=sin(x)/x; 
g2(x):=x*sin(1/x);

limit(g1(x), x, 0);
limit(g2(x), x, 0) ;

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