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Limits of x/ln(x)

  • #1
212
2

Homework Statement


Hello all,

I am having hard time with limits.

1. limx->1- x/ln(x)

2. limx->1+ x/ln(x)

Homework Equations




The Attempt at a Solution


1. limx->1- x/ln(x)
= 1-/ln(1-)
ln(1-) = 0-

I seriously dont understand why ln(1-) = 0-

2. limx->1+ x/ln(x)
= 1+/ln(1+)
ln(1+) = 0+

I seriously dont understand why ln(1+) = 0+


thanks
 

Answers and Replies

  • #2
941
394
Do you know what the natural logarithm graph looks like?
 
  • #3
212
2
Do you know what the natural logarithm graph looks like?
yes I do, doing limits with a graph is easy, I have to resolve this by doing algebra.
 
  • #4
941
394
You say you don't understand why ln(1) = 0. This is common knowledge about the logarithmic function. You have a function approaching 0 in the denominator and a function approaching 1 in the numerator. What does that tell you?
 

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