What is it limit as #xrarr9#? #sqrtr/((r-9)^4)#
1 Answer
Feb 19, 2018
the limit does not exist (it diverges)
Explanation:
We seek the limit:
# L = lim_(r rarr 9) sqrt(r)/(r-9)^4 #
We note that if we substitute
However, this alone tells us that there is an asymptote of the function
# lim_(r rarr 9) sqrt(r)/(r-9)^4 \ ~ \ 3/0 # as#r rarr 9#
In other words
# lim_(r rarr 9) sqrt(r)/(r-9)^4 rarr oo#
And we conclude that the limit does not exist (it diverges)