## nickymarden Group Title ... 2 years ago 2 years ago

1. nickymarden Group Title

$\lim_{x \rightarrow 0} cosx-1/x$

2. Thomas9 Group Title

cos(x-1/x)?

3. nickymarden Group Title

(cosx-1)/x

4. Thomas9 Group Title

5. TuringTest Group Title

are you allowed to use l'Hospitals rule?

6. nickymarden Group Title

nope. Professor said that if we use it he won't consider the answer

7. TuringTest Group Title

well this limit is very well-known, and is usually proven geometrically, so... I'm not sure what we want to do here

8. nickymarden Group Title

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.

9. Thomas9 Group Title

You can write cos(x) as a series, that'll work.

10. TuringTest Group Title

^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/

11. TuringTest Group Title

so there are technically 3 ways of finding the answer

12. nickymarden Group Title

yep. MIT always saving my life. Thanks again :P

13. TuringTest Group Title

that is the long way though^ the "short" way is l'Hospitals rule

14. TuringTest Group Title

but you're welcome :)