L'Hopital's rule
posted by Anonymous on .
Find lim x>1+ of [(1/(x1))(1/lnx)].
Here is my work...
=(lnx(x1)) / ((x1)(lnx))
=(lnx1) / (lnx+ (x+1)/x)
This becomes(1/x) / ((1/x)+(1/x^2))
which becomes 1/ (1/x^2)
This equals 1/2. I understand the answer has to be 1/2, but I am having trouble figuring out where that negative sign is coming from. What have I missed? Thank you in advance for your assistance.

=(lnx(x1)) / ((x1)(lnx))
How did you get to the next line?