# Exercici 04.3

## Apartat a)

kill(all)$

x[n]:=(sin(n))/n;

L=limit(x[n], n, inf);

## Apartat b)

kill(all)$

x[n]:=(n!)/n^n;

L=limit(x[n], n, inf);

## Apartat c)

kill(all)$

x[n]:=(1/((1/n^2)+(1/n)))-(1/((1/n^4)+(1/n)));

L=limit(x[n], n, inf);

## Apartat d)

kill(all)$

x[n]:=(2^n + 3^n)/(2^n - 3^n);

L=limit(x[n], n, inf);

## Apartat e)

kill(all)$

x[n]:=log((n-2)/(n+2))^n;

L=limit(x[n], n, inf);

## Apartat f)

kill(all)$

x[n]:=((n+2)/(2*n))^(sin(1/n));

L=limit(x[n], n, inf);

## Apartat g)

kill(all)$

x[n]:=((n^2 + a*n +1)/(n^2))^n;

L=limit(x[n], n, inf);

## Apartat h)

kill(all)$

x[n]:=(log(%e^n + %e^(-n)))/n;

L=limit(x[n], n, inf);