Thursday, December 20, 2012

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
.

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