Expert: Ahmed Salami - 12/11/2005

Question
can you find anther simple way to analyis

lim (1-cosx)/x^2
x_ 0  

Answer
Hi Muhammed,
Inserting the limit directly results in the indeterminate form 0/0
We therefore insert the limit after differentiating top and bottom,
this is called the l'hopital Rule.
Therefore,
lim(x_0) 1 - cosx / x^2 = lim(x_0) sinx /2x
this still results in 0/0, we then apply the rule again to get
lim(x_0) cosx/2
inserting the limit now gives our final answer of
lim(x_0) 1 - cosx / x^2 = 1/2
I hope i have helped, you can always get back to me.
Regards.