# Exercici 08.5

kill(all)$

a)

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

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

b)

kill(all)$

f(x):=(exp(2*x)*sin(2*x))/(exp(3*x)*sin(3*x));

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

c)

kill(all)$

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

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

d)

kill(all)$

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

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

f1(x):=x*sin(1/x);
f2(x):=sin(x)/x;

limit(f1(x), x, 0);
limit(f2(x), x, 0);

'limit(f(x), x, 0) = limit(f1(x), x, 0)/limit(f2(x), x, 0);

e)

kill(all)$

f(x):=x*(log(x)^2);

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

f)

kill(all)$

f(x):=(1/sin(x)) - 1/x;

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