That looks fine!
Notice the denominator of the limit it has to be else you don't have the indeterminate form but offcourse it doesn't make a difference to apply l'Hopital's rule.
Use analytical methods to evaluate the following problem.
the answer to the limit is
I have been taking a stab at it for quite a while. I think I figured it out but I a want to make sure the methods to how I got the answer were proper.
First thing, Apply L' Hoptial's rule to make the -2 and the + disappear
= =
I make powers have the same denominator
I get rid of the exponent denominator by applying an exponent of the power 5 to the limit. I also make it positive for simplicity.
=
I observe the limit which will equal 1 and multiply by -6/5
=
=