Homework Help: Evaluate lim of f.

1. Feb 17, 2012

mathlike

1. The problem statement, all variables and given/known data[/b]

Evaluate lim x goes to ∞ positive
((x-1)*(bx-1)/(b-1))(1/x)

2. Relevant equations

3. The attempt at a solution[/b]
I try to take log but it does not seem to work

Last edited: Feb 17, 2012
2. Feb 17, 2012

DivisionByZro

Is this the problem?

$$\lim_{x\to\infty}\frac{(b^{x}-1)}{x(b-1)}^{\frac{1}{x}}$$

3. Feb 18, 2012

mathlike

Yes. I tried taking log but to no avail

4. Feb 18, 2012

alanlu

5. Feb 18, 2012

mathlike

still cannot solve it. Need help guys! Appreciated.

6. Feb 18, 2012

alanlu

To clarify, is it this?
$$\lim_{x\to\infty}\left(\frac{b^{x}-1}{x(b-1)}\right)^{\frac{1}{x}}$$
Or is it this?
$$\lim_{x\to\infty}\frac{(b^{x}-1)^{\frac{1}{x}}}{x(b-1)}$$

For the latter, note that for all x > 1, b > 1,
$$0 \leq (b^{x}-1)^{\frac{1}{x}} \leq b$$
For the former, I am not immediately sure.

Last edited: Feb 18, 2012
7. Feb 18, 2012

Dick

Judging by you initial parentheses I think you actually mean. $$\lim_{x\to\infty} \big( \frac{b^{x}-1}{x(b-1)} \big) ^{\frac{1}{x}}$$.

And can you show why taking the log isn't working. Or something?

8. Feb 19, 2012

mathlike

I simplified it down to calculate
limx->infinity (b^x-1)/x
......can help me to proceed?

9. Feb 19, 2012

Dick

I don't see how you got that. You need to show us.