# Looking for the limit of a function g(x). Algebra of Limits problem. Analysis 4420

Define $g: (0,1)\to\mathbb{R}$ by $g (x)=\frac{\sqrt{1+x}-1}{x}$. Prove that g has a limit at 0 and find it.
In my course we are given only the definition of a limit, namely that $g$ has a limit at $x_0$ iff there exists a $\delta$ such that given any $\epsilon >0$ we have
$|g(x)-L|<\epsilon$ for all $0<|x-x_0|<\delta$.