Calculating Limit Help

[FraPin]

Hi everyone, I am stuck on this limit Lim x->inf ((x^2-1)/(x^2+3x-1))^(x-1) , could someone help me resolving this without using de l`hopital rule?

 

[Deleted member 4993]

Hi everyone, I am stuck on this limit Lim x->inf ((x^2-1)/(x^2+3x-1))^(x-1) , could someone help me resolving this without using de l`hopital rule?

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem

 

[Dr.Peterson]

Hi everyone, I am stuck on this limit Lim x->inf ((x^2-1)/(x^2+3x-1))^(x-1) , could someone help me resolving this without using de l`hopital rule?

What methods are available to you besides L'Hopital? And are you instructed not to use that, or is that just your preference?

 

[Steven G]

Hint: I would break it up into a product

 

[blamocur]

I'd start by observing that
[math]\left(\frac{x^2-1}{x^2+3x-1}\right)^{x-1} = \left(1 - \frac{3x}{x^2+3x-1}\right)^{x-1}[/math]Can you see some similarity with a well-known but non-trivial limit?

 

[Steven G]

OH, the whole thing is raised to the (x-1) power!. I thought that just the denominator was!