Question

Question #54339

Answer 1

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`.

`(ln x)' = 1/x > 0`.

So, `ln x uarr` as `x uarr`.

And so, as `x to oo, ln x to oo`.

Of course, the rate is `1/x darr` 0, as `x to oo`.

As `x to 0, ln x to -oo, x =0 darr` is the asymptote to the graph.