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

  • Thread starter frasifrasi
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Hence, ln(x) grows faster than a linear function, and faster than any polynomial function, as x goes to inifnity.In summary, the limit of ln(x) as x approaches negative infinity is infinity, as x approaches zero from the left, the limit is negative infinity, and as x approaches zero from the right, the limit is infinity. This can be seen by visualizing the graph of ln(x) and understanding its behavior as x approaches different values.
  • #1
frasifrasi
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Brief, basic -- lim question...

So, i know this is too basic, but can anyone tell me what the lim of ln(x) is as x approaches
-infinity
-neg infinity
-zero (from left and right)

--> I know I am supposed to know these, but I think I might be confusing them...

Thank you!
 
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  • #2
You can do this analytically, just by visualizing the graph of the function.
-As x increases, the natural log of x also increases without bound.
-Are negative numbers part of your domain?
-What happens to values of ln(x) as x approaces 0? Just look at a graph of the parent function.
 
  • #3
I wouldn't call that analytic. I would think of ln(x) as the inverse of exp(x) and exp(x) has derivative strictly greater than 1 for all x>0.
 

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