Evaluate each of the following (possibly infinite) limits or explain why it does not exist
lim x→5− lnx/(x−5)^2

Question

Evaluate each of the following (possibly infinite) limits or explain why it does not exist
lim x→5−  lnx/(x−5)^2

anonymous · Answer

$$\lim_{x \rightarrow 5-} \ln x/(x-5)^2$$

anonymous · Answer

$$ \lim_{x \rightarrow 5-} {\ln x \over (x-5)^2} = {\ln 5 \over 0^2} = \infty$$

anonymous · Answer

i think the denominator cant be 0 right ?

anonymous · Answer

Yes ... you are right!!

Also try to graph the function
$$ {\ln x \over (x-5)^2}$$

at x -> 5, the graph goes up to infinity ( where it diverges)

anonymous · Answer

can u show me some working how to do it ?

anonymous · Answer

http://www.wolframalpha.com/input/?i=plot+log%28x%29%2F%28x-5%29^2+from+4+to+6

anonymous · Answer

ty

anonymous · Answer

you are welcome :D