What is the limit as x approaches infinity of ln(x)?

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Infinity.

Explanation:

As you can see from these 2 graphs of ##ln(x)##:

It seems that as ##x## continues to instigate in the assured order, the appraise of ##y## keeps increasing, although unwillingly. You could so try plugging in larger and larger total into the ##ln(x)## power and see that it continues to conclusion in larger and larger answers. Because the ##y## appraise continues increasing to ##oo##, the expression of ##ln(x)## as ##x## instigates very far to the upupright (such as close ##oo##), is so ##oo##:

##lim_(x->oo) ln(x) = oo##

Explanation 2:

You can so appear at the derivative of ##ln x## which is ##1/x##. Since this derivative is assured, it resources the power is eternally increasing plain if it is very inferior. In conditions of basic powers, ##ln x## has the slowest development. The simply way to get slower growing powers is to keep composite powers such as ##ln(ln x)##.

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