Question

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

Answer 1

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

Answer 2

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

Answer 3

i think the denominator cant be 0 right ?

Answer 4

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)

Answer 5

can u show me some working how to do it ?

Answer 6

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

Answer 7

ty

Answer 8

you are welcome :D