1. ## Limit

Hi everybody,

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

And great thanks.

2. ## Re: Limit

Originally Posted by sciencebetter
f is a function such as $\displaystyle \lim_{x\to x_0}$ f(x)=A, and g is also a function such as $\displaystyle \lim_{x\to x_0} g(x)=B$, how to show that $\displaystyle \lim_{x\to x_0} f(x)+g(x)=A+B.$.
$\displaystyle |(f(x)+g(x))-(A+B)|\le |f(x)-A|+|g(x)-B|$
You have "control" over the size of both $\displaystyle |f(x)-A|~\&~|g(x)-B|$.