Question

Evaluate the following limit .
lim x->5- lnx/(x-5)^2

Answer 1

are you familiar with the l'hospital rule?

Answer 2

nah

Answer 3

you cannot use l'hopital here

Answer 4

the denominator goes to zero, but the numerator does not, so no limit

Answer 5

I believe it's infinity.
\[\begin{align}\lim_{x\rightarrow 5} \ln x = \ln 5\\
\lim_{x\rightarrow 5} (x-5) = 0\end{align}\]
Hence you have a positive real number over a very, very small positive real (the square ensures the denominator is positive), implying the limit is infinity.