## nickymarden 3 years ago ...

1. nickymarden

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

2. Thomas9

cos(x-1/x)?

3. nickymarden

(cosx-1)/x

4. Thomas9

5. TuringTest

are you allowed to use l'Hospitals rule?

6. nickymarden

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

7. TuringTest

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

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

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

10. TuringTest

^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

so there are technically 3 ways of finding the answer

12. nickymarden

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

13. TuringTest

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

14. TuringTest

but you're welcome :)