Does ln of a Fraction Approach Infinity as R Increases?

[Gamma]

Hi,



What is the limit of
ln(\frac{1+1/ \sqrt(1+1/R)}{1-1/ \sqrt(1+1/R})

as R reaches infinity.


(latex did not show it very well. But the numerator is same as denominator except there is a + sign instead of a - sign.

As R reaches infinity the argument of the ln reaches infinity. Is the limit also infinity?





Thank You.

Gamma.

 

[VietDao29]

Hi,



What is the limit of ln(\frac{1+1/ \sqrt(1+1/R)}{1-1/ \sqrt(1+1/R})

as R reaches infinity.


(latex did not show it very well. But the numerator is same as denominator except there is a + sign instead of a - sign.

As R reaches infinity the argument of the ln reaches infinity. Is the limit also infinity?





Thank You.

Gamma.

If your LaTeX image is big, don't use [ itex ], use [ tex ] instead.
So do you mean:
\lim_{R \rightarrow \infty} \ln \left( \frac{1 + \frac{1}{\sqrt{1 + R}}}{1 - \frac{1}{\sqrt{1 + R}}} \right)? Or what?
If you mean that, then if R \rightarrow \infty, then \sqrt{1 + R} \rightarrow \ ?, \frac{1}{\sqrt{1 + R}} \rightarrow \ ?, 1 \pm \frac{1}{\sqrt{1 + R}} \rightarrow \ ?.
Can you go from here? :)

 

[HallsofIvy]

Gamma, I've taken the liberty of editing your Latex by changing "itex" to "tex". "itex" doesn't work well with complex fractions.

As VietDao29 told you- the argument inside the ln does NOT go to infinity. It should be sufficient to see what happens to 1/R as R goes to infinity.