Question #54339

1 Answer
A. S. Adikesavan
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#.

#(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.

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