Answer
$0.5$
Work Step by Step
We need to build a table that shows the values of $x$ close to $0$ from the left and right sides and the values of $f(x)$ for those values of $x$.
$ x= -0.1..........., x= 0.111111$
This gives:
$ f(x)= 0.513167019,......f(x)= 0.486832993$
From the table, we have
$\lim_\limits {x \to 0} \dfrac{\sqrt {x+1}-1}{x}=0.5$
