## Proposition 6.1.7: Properties for limits of Functions

If

*f(x)*exists, the limit is unique.
*[ f(x) + g(x) ] =
f(x) +
g(x)*,
provided that
* f(x)*
and
* g(x)*
exist.

*[ f(x) g(x) ] =
f(x)
g(x)*,
provided that
* f(x)*
and
* g(x)*
exist.

*[ f(x) / g(x) ] =
f(x) /
g(x)*,
provided that
* f(x)*
and
* g(x)*
exist and
*g(x) # 0*.