# Find the limit of

1. Jan 31, 2012

### daveronan

1. The problem statement, all variables and given/known data
Find the limit of the following function

lim w→∞ (1 + z/w)w

2. Relevant equations

3. The attempt at a solution

lim w→∞ w ln(1 + z/w)

Not sure where to go next...

Thanks
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jan 31, 2012

### daveronan

I've tried l'Hopitals rule, but I don't think I'm any closer.

3. Jan 31, 2012

### A. Bahat

Can you show how you tried l'Hopital's rule? Because I tried it and it worked.

4. Jan 31, 2012

### daveronan

w/(1 + z/w) + 1/ln(1 +z/w)

5. Jan 31, 2012

### daveronan

I think I may have forgot the chain rule...

6. Jan 31, 2012

### Dick

w ln(1 + z/w) has the form infinity*0. You'll want to arrange it into an infinity/infinity form before you do l'Hopital. Can you show how you tried to apply it?

7. Jan 31, 2012

### daveronan

lim w→∞ w.ln(1/w*(w+z))

8. Jan 31, 2012

### daveronan

After l'Hopital I'm getting lim w → ∞ ( -z/(w+z) + ln(1 + z/w))

This doesn't seem to help, not unless I'm doing something stupid.

9. Jan 31, 2012

### Dick

That's still infinity*0. Try rearranging it into $\frac{ln(1+\frac{z}{w})}{\frac{1}{w}}$. That's 0/0.

10. Jan 31, 2012

### daveronan

I've done that, but it still brings me to this.

11. Jan 31, 2012

### daveronan

Wait, the penny dropped. The answer is z. You multiply across by -(w+z) :) Thanks for all your help.!!

12. Jan 31, 2012

### Joffan

... not forgetting you took the logarithm at the start.