Here's the question you clicked on:
nickymarden
...
\[\lim_{x \rightarrow 0} cosx-1/x\]
I had my answer ready for the other one, I need to think about this one.
are you allowed to use l'Hospitals rule?
nope. Professor said that if we use it he won't consider the answer
well this limit is very well-known, and is usually proven geometrically, so... I'm not sure what we want to do here
there are 2 ways to finding the answer, and I know it's 0. I know one of them, wich takes too long, i want the other.
You can write cos(x) as a series, that'll work.
^that is true, that would be the only other way to prove it besides the geometric way which is given here: http://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/part-a-definition-and-basic-rules/session-7-derivatives-of-sine-and-cosine/
so there are technically 3 ways of finding the answer
yep. MIT always saving my life. Thanks again :P
that is the long way though^ the "short" way is l'Hospitals rule
but you're welcome :)