# Homework Help: Continuity of functions

1. Nov 17, 2012

### Felafel

hi everyone, I've found this exercise on a text book and it doesn't resemble any exercise I've seen before. I just want to know how to proceed, you don't have to solve it for me :)

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

Study the continuity of the following functions, defined by:

1- f(x) = lim (n^x-n^-x)/(n^x+n^-x) x∈|R
n->+∞

2- f(x) = lim [ln(e^n+x^n)]/n x∈|R
n->+∞

3. The attempt at a solution

A function is continuos if its limit L exists and it equals f(L).
But the limit here is to +∞!
So, after computing the two limits for the given n->+∞, how do I go on studying the finction?

Many thanksss

2. Nov 17, 2012

### tiny-tim

Hi Felafel!
You'll get the value of f(x) for various values of x.

Draw the graph (in your head, if it's easy), and it should be obvious whether it's continuous!

3. Nov 18, 2012

### Felafel

thank you :)!
just.. random values?

4. Nov 18, 2012

### tiny-tim

yup!

usually works!

5. Nov 18, 2012

### HallsofIvy

If you divide both numerator and denominator by $n^x$, you get
$$\frac{1- n^{-2x}}{1+ n^{-2x}}$$
Now suppose x> 0 and look at three cases, 0< x< 1, x= 1, x> 1.

Then divide both numerator and denominator by $n^{-x}$ to get
$$\frac{n^{2x}- 1}{n^{2x}+ 1}$$
And do similary for x< 0.