Question

help? step by step? (:

limit as x approaches 0 of (1-cos(x))/(x^2)

Answer 1

l'hopital will work nicely
first check that if you replace \(x\) by 0 you get \(\frac{0}{0}\) which you do

Answer 2

then take the derivative top and bottom, bet
\[\frac{-\sin(x)}{2x}\] which, if you replace \(x\) by \(0\) still gives \(\frac{0}{0}\) so it is l'hopital again

Answer 3

this time the derivative gives you
\[\frac{-\cos(x)}{2}\] and now replacing \(x\) by \(0\) gives the limit as \(-2\)

Answer 4

It's actually 1/2 (:

Answer 5

yeah, that one!

Answer 6

lol (; I got the point though.