1. The problem statement, all variables and given/known data limit as x goes to infinity of (1/x^2) - (cscx)^2 2. Relevant equations 3. The attempt at a solution I made it so the denominator is x^2, but then it would 1-inf/inf which isn't indeterminate. i need help setting it up so it would be in indeterminate form. thanks.
You probably mean lim x->0, right? Just make a common denominator and combine those two terms into a single fraction. It's probably easier to write 1/sin(x)^2 instead of csc(x)^2, but it will still take several derivatives before you get a nonindeterminant answer from l'Hopital.
Then tell me about the limiting behavior of 1/x^2 and csc(x)^2 as x->inf. Is that expression really indeterminant?