another limit using l'hopitals

magnifik

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.

Dick

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.

magnifik

nope, the question states lim x-> inf

Dick

Then tell me about the limiting behavior of 1/x^2 and csc(x)^2 as x->inf. Is that expression really indeterminant?

magnifik

that's what my original problem was

Dick

Sketch a graph of each one. The limiting behavior should be visually obvious.

Altabeh

The limit does not exist by any means. If needed, a proof can be given.

AB