limits de funcions

lim [ x --> 1 ]-[ ( (x^{n}+(-1))/(x+(-1)) ) ] = n
lim [ x --> 1 ]-[ ( (x^{(1/n)}+(-1))/(x+(-1)) ) ] = (1/n)


lim [ x --> 1 ]-[ ( (x^{n}+(-1))/(x^{m}+(-1)) ) ] = (n/m)
lim [ x --> 1 ]-[ ( (x^{(1/n)}+(-1))/(x^{(1/m)}+(-1)) ) ] = (m/n)


lim [ x --> 1 ]-[ ( ( (x+(-1))·...(n)...·(x^{n}+(-1)) )/(x+(-1))^{n} ) ] = n!
lim [ x --> 1 ]-[ ( ( (x+(-1))·...(n)...·(x^{(1/n)}+(-1)) )/(x+(-1))^{n} ) ] = (1/n!)


lim [ x --> 1 ]-[ ( ( x+...(n)...+x^{n}+(-n) )/(x+(-1)) ) ] = ∑ k = (1/2)·n(n+1)
lim [ x --> 1 ]-[ ( ( x+...(n)...+x^{(1/n)}+(-n) )/(x+(-1)) ) ] = ∑ (1/k)


lim [ x --> 0 ]-[ ( ( 1^{x}+...(n)...+n^{x}+(-n) )/x ) ] = ln(n!)
lim [ x --> 0 ]-[ ( ( 1^{x}+...(n)...+(1/n)^{x}+(-n) )/x ) ] = (-1)·ln(n!)


indicacions:
(x^{n}+(-1)) = (x+(-1))·(1+...(n)...+x^{(n+(-1))})
(x+(-1)) = (x^{(1/n)}+(-1))·(1+...(n)...+x^{( (n+(-1))/n )})
a^{x} = e^{ln(a)·x}