Calculate the limit (1-cosx)/x^2 , x->0

The limit has to be
determined.

If we substitute x = 0, the result
is the indeterminate form . In this case it is possible to use
l'Hospital's rule and replace the numerator and denominator with their
derivatives.

x

The limit is
now:

x/(2x)

If the substitution x = 0 is made here, the result
is again the indeterminate form . Using l'Hospital's rule, replace the numerator
and denominator with their derivatives. This
gives:

x/2

Substituting x = 0 gives the result
1/2.

The limit
.