Question

f(x)= (lnx)/(1+(lnx)^2) for x in (0, ∞). find lim(x-->0+) and lim(x-->∞)

Answer 1

both limits go to 0

Answer 2

to show it algebraically , use L'Hopitals rule
differentiate top and bottom separately
\[\rightarrow \frac{\frac{1}{x}}{\frac{2\ln(x)}{x}} = \frac{1}{2 \ln(x)}\]
then evaluating this as x->0+ and x->inf

Answer 3

thanks so much for your help :) I had been working on this problem for a while now.