Limit Question: lim x ---> 0 ( 1 / x^ 2 - ( cot x ) ^ 2 )

[grapz]

lim x ---> 0 ( 1 / x^ 2 - ( cot x ) ^ 2 )

This is in the form infinity - infinity.

I tried making a subsituation to try to make it into 0/0 or infinity/infinity, but it doesnt' seem to work.

i did let t = 1/ x

can someone give me some insight

 

[royhaas]

Re: Hard Limit Question

Use a series expansion.

 

[grapz]

Sorry can you explain what a series expansion is.

This was a homework question in a calculus textbook, the question is indeed to use l'hopitals rule and they havn't explained any series expansion so there must be another method

 

[Deleted member 4993]

lim x ---> 0 ( 1 / x^ 2 - ( cot x ) ^ 2 )

\(\displaystyle Lim(x -> 0) [\frac{1}{x^2} - cot^2x\ ]\)

\(\displaystyle = Lim(x -> 0) [\frac{1}{x^2} - \frac{1}{tan^2x}\ ]\)

Continue.....