Thread: question regarding limit to infinity

Hi my question is this:
If two functions, say f and g are defined on an open set , where
and ,
how can I show that

Originally Posted by dannyboycurtis

Hi my question is this:
If two functions, say f and g are defined on an open set , where
and ,
how can I show that

Since as , then , which is by definition.

(See tonio's post below for a full-blown -proof.)

Originally Posted by dannyboycurtis

Hi my question is this:
If two functions, say f and g are defined on an open set , where
and ,
how can I show that

Choose any e > 0 ==> there exists a real number M s.t. |f(x) - L| < e whenever x > R.

Since g(x) --> oo when x --> oo there exists a number T s.t. g(x) > R whenever x > T ==> for ANY x > T you get

|f(g(x)) - L| < e , and this means f(g(x)) --> L when x --> oo

Tonio

Originally Posted by tonio

Choose any e > 0 ==> there exists a real number M s.t. |f(x) - L| < e whenever x > R.

You mean there exists a real number R s.t...

Or he means "whenever x> M".