Limits: Why doesn't l'hopital's rule work? ?

Question

i have a weird limit problem

lim (sqrt x)/(x-16)

x --> 16

when i calculate it i use l'hopital's rule since the original is in interdeterminate form if i sub in 16 so i take the derivative of numerator and denominator respectively and i get 0.5x^-0.5/1 then i substitute in 16 and i get limit as 1/8

but when i graph it i find that the limit is actually infinity

hmm.. seems like l'hopital rule is working...

why isn't l'hopital's rule working and when do i know that it will not work?

thanks in advance

Answer 1

L'Hospital's rule works as long as the form of the fraction is [0/0] or [infinity/infinity].  In this case, the form is 4/0, which already tells us the limit does not exist.