Definition of limit as x approaches infinity

Hi everyone!

I am not quite understanding the definition of a limit L as x approaches infinity. The definition states the following:

" We say that f(x) has the limit** L as x approaches infinity** and write

lim _{x->∞ }f(x) = L

if for every number **Є** > 0 there exists a corresponding number *M* such that for all x

x > M -> |f(x) - L| < Є "

That is the definition from the book, and I don't understand what they mean by the number M. Can anyone explain what the number M is?

Thanks!

Re: Definition of limit as x approaches infinity

Quote:

Originally Posted by

**Nora314** Hi everyone!

I am not quite understanding the definition of a limit L as x approaches infinity. The definition states the following:

" We say that f(x) has the limit** L as x approaches infinity** and write

lim _{x->∞ }f(x) = L

if for every number **Є** > 0 there exists a corresponding number *M* such that for all x

x > M -> |f(x) - L| < Є "

That is the definition from the book, and I don't understand what they mean by the number M. Can anyone explain what the number M is?

Thanks!

M is an arbitarily large number that depends on epsilon.

Just like delta was an arbitarily small number that depends of epsilon.

So they are basically saying if we pick M big enough that for any x bigger than M f(x) is getting close to the limit (read less then epsilon)