I'm supposed to solve this exercise: 1
So at first i though you could just rewrite the term by factoring out the n^4 below the root and and then let everything inside the root except the 1 evaluate to 0 by taking the limit (and then let the n^2 cancel each other out and get 1 as result). 4
This is wrong (altough i'm not sure yet in which way/how the formulas were misapplicated). I also have the solution to the exercise: 5
My central understanding problem is in the last line of the solution: Why is it correct to let take individual limits inside the root and let everything (except the 1) evaluate to 0 in this situation, but not in the "original" formula (as i did)?
Thanks for any help
original title (if that’s more understable) (without character-limit): Limits: Why can you sometimes factor out the highest exponent under a root, and then let everything else inside the root evaluate to 0 when taking the limit, but othertimes (apparently) not?