Question

I need to find the limit as x approaches zero for cos^2 x / x

Answer 1

does it not exist ?

Answer 2

This might help - https://www.symbolab.com/solver/limit-calculator/%5Clim_%7Bx%5Cto0%7D%5Cleft(%5Cfrac%7Bcos%5E%7B2%7D%5Cleft(x%5Cright)%7D%7Bx%7D%5Cright)/?origin=suggestion

Answer 3

I would have thought zero based on L'Hospitals., but it diverges

Answer 4

start by actually setting x to zero and seeing what that gives....!

Answer 5

Come to think of it, we have 1/0 not 0/0 so L'Hopital's would apply when we have 0/0. Since for 1/0 (due to the x term in the denominator) and approaching 0 from the right we have +inf and approaching from the left we have -inf, there is no limit and the limit does not exist.

I forgot that 1/0 is NOT in indeterminate form

http://en.wikipedia.org/wiki/Indeterminate_form

Answer 6

thank you

Answer 7

You're welcome