# Limit

• October 14th 2012, 09:30 AM
sciencebetter
Limit
Hi everybody,

f is a function such as $\lim_{x\to x_0}$ f(x)=A, and g is also a function such as $\lim_{x\to x_0} g(x)=B$, how to show that $\lim_{x\to x_0} f(x)+g(x)=A+B.$.

And great thanks.
• October 14th 2012, 09:45 AM
Plato
Re: Limit
Quote:

Originally Posted by sciencebetter
f is a function such as $\lim_{x\to x_0}$ f(x)=A, and g is also a function such as $\lim_{x\to x_0} g(x)=B$, how to show that $\lim_{x\to x_0} f(x)+g(x)=A+B.$.

$|(f(x)+g(x))-(A+B)|\le |f(x)-A|+|g(x)-B|$
You have "control" over the size of both $|f(x)-A|~\&~|g(x)-B|$.