# Exercici 06.7

## apartat a)

kill(all)$

f(x):=1/(1-x) - 3/(1-x^3);

limit(f(x), x, 1);

## Apartat b)

kill(all)$

f(x):=(x^(2/3) - 2*x^(1/3) +1)/(x-1)^2;

limit(f(x), x, 1);

## Apartat c)

kill(all)$

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

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

## Apartat d)

kill(all)$

f(x):=(2*x)/sin(x) - (x^2/4)/(1-cos(x)) ;

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

## Apartat e)

kill(all)$

f(x):=((x^2 - 1)/(x^2 + 1))^(x^2) ;

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

## Apartat f)

kill(all)$

f(x):=(x^2 - (a+1)*x + a)/(x^3 - a^3) ;

limit(f(x), x, a);

## Apartat g)

kill(all)$

f(x):=(sqrt((1+ a*x)*(1 + b*x)) - 1)/(x) ;

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

## Apartat h)

kill(all)$

f(x):=((a^(1/x) + b^(1/x))/(2))^(x) ;

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