# Thread: [SOLVED] Why is limit of natural log equal to ln of limit?

1. ## [SOLVED] Why is limit of natural log equal to ln of limit?

Why is that

$\lim _{x\to -\infty} \frac{x+1}{x-1} = \ln(\lim _{x\to -\infty} \frac{x+1}{x-1})$

Can anyone kindly explain it?

2. Originally Posted by x3bnm
Why is that

$\lim _{x\to -\infty} \frac{x+1}{x-1} = \ln(\lim _{x\to -\infty} \frac{x+1}{x-1})$

Can anyone kindly explain it?
It isn't. The first one is 1 the second is 0[/tex]

3. Sorry the expression was wrong in my last post. Edited one is :

$\lim _{b\to -\infty} (\ln(|\frac{b-1}{b+1}|) ) = \ln(\lim _{b\to -\infty} \frac{b-1}{b+1})$

I found them Thomas' Calculus solution book as part of solving a integral(Chapter 8.8 exercise9). But why are they equal?

4. Because ln(x) is continous for every $x>0$

5. Because ln(x) is continous for every $x > 0$
Can you elaborate on this?

6. The function is not discontinuous on any interval greater than 0, or does not have any asymptotic holes on intervals greater than 0, simply look at the graph as x is > 0 and it continues to reach infinity in terms of limits

Finding the graph is simple, just use a calculator or manually find the "sequence of terms" for each x, like x = 1, x = 2, x = 3...and so on to make the graph and youll see why

7. Thanks hjortur and RockHard. I get it now.

8. One of the definitions/implications of continuity is that if you have a sequence $\{x_n\}$ such that $\lim_{n\to\infty}x_n=x$, then $\lim_{n\to\infty}f(x_n)=f(x)$