# Homework Help: Show that f is continuous at every point in R

1. Sep 28, 2011

### acacia89

Suppose a function f : R → R satisfy f(x + y) = f(x) + f(y) and f is continuous
at x = 0: Show that f is continuous at every point in R.

(Hint: Using the fact that
lim f(x) = l implies
x→x0
limf(x0+h)= l
h→0 )

2. Sep 28, 2011

### LCKurtz

You need to show us what you have tried so we can see how to help you.

Show that $\lim_{n\to\infty}(1+\frac{r}{n})^n=e^r$