# Question #54339

Feb 7, 2017

See explanation. See graph for the features in the explanation..
graph{(ln x-y)(x+.001y)=0 [-10, 10, -5, 5]}

#### Explanation:

ln x is real and differentiable, for $x > 0$.

$\left(\ln x\right) ' = \frac{1}{x} > 0$.

So, $\ln x \uparrow$ as $x \uparrow$.

And so, as $x \to \infty , \ln x \to \infty$.

Of course, the rate is $\frac{1}{x} \downarrow$ 0, as $x \to \infty$.

As $x \to 0 , \ln x \to - \infty , x = 0 \downarrow$ is the asymptote to the graph.