Question

...

Answer 1

\[\lim_{x \rightarrow 0} cosx-1/x\]

Answer 2

cos(x-1/x)?

Answer 3

(cosx-1)/x

Answer 4

I had my answer ready for the other one, I need to think about this one.

Answer 5

are you allowed to use l'Hospitals rule?

Answer 6

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

Answer 7

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

Answer 8

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.

Answer 9

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

Answer 10

^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/

Answer 11

so there are technically 3 ways of finding the answer

Answer 12

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

Answer 13

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

Answer 14

but you're welcome :)