Question

Show, without graphing, that the limit as x approaches zero from the positive side of natural log x over x is negative infinity.

Answer 1

\[\lim_{x \rightarrow 0^{+}}\frac{ lnx }{ x }=-\infty \]

Answer 2

What is posted abouve is what one of my students answered.

Answer 3

What would you do to answer it?

Answer 4

1. the domain of the function is x>0
2. denominator is always +ve
3. for numberator, \(\ln x=0\) for \(x=1\).
for \(x>1,\quad\ln x>0\)
for \(0<x<1,\quad \ln x<0\)
4. thus,in the interval \(0<x<1\), the limit is -ve.
then you throuw in a graph