Hello, I'm trying to find the limit(as n approaches 0) of [1-cos(n)]/(n^2). I have done a few of these before and haven't had to much trouble, but they all have been as n approaches infinity.
I think the n approaches 0 is confusing me.
The Attempt at a Solution
I let n=0 and was left with 0/0, which would justify the use of L'Hopital's Rule. I then differentiated the numerator and denominator and was left with sin(n)/2n. Now do I let n=0, if so I would just be left with 0/0 again. I don't know where to go with this.
I am also having trouble with a another similar question, being finding the limit(as n approaches 0) of (n^2)sin^2(1/n). What sort of equations could I use as the less than and more than equations and how would the standard limits rules for n approaches infinity come into play?
Thanks in advance for any help or advice.