bothering problems

[kavlas]

Hi everyone

 

There two problems that bother me for quite some time.

 

1)If [math]\lim_{x\to\infty}\frac{f(x+1)}{f(x)}=2[/math] then find [math]\lim_{x\to\infty}\frac{f(x+2)}{f(x-2)}[/math].

 

2) I do not know if this the right place to ask for this problem but here it goes.

 

Can we prove the De Morgan law?

 

Thank you

[Mr Skeptic]

Find [math]\lim_{x\to\infty}\frac{f(x+2)}{f(x+1)}\frac{f(x+1)}{f(x)}\frac{f(x)}{f(x-1)}\frac{f(x-1)}{f(x-2)}[/math]

[kavlas]

Why?

[Mr Skeptic]

Why not?

[kavlas]

Why not?

 

I am sorry i cannot see why you are doing that.

[Mr Skeptic]

Well, cancel out the terms and see what you get. On the other hand, can you figure out what the limit of the individual fractions would be, and then multiply them together?