# What is the limit of limxto1(sqrt(x+3)-2)/(x-1)?

Mar 28, 2018

I got: $\frac{1}{4}$.

#### Explanation:

Have a look:

we could also try this:
Let us multiply top and bottom by $\sqrt{x + 3} + 2$, we get:
${\lim}_{x \to 1} \left(\frac{\sqrt{x + 3} - 2}{x - 1}\right) \frac{\sqrt{x + 3} + 2}{\sqrt{x + 3} + 2}$
we would get:
${\lim}_{x \to 1} \frac{\left(x + 3\right) - 4}{\left(x - 1\right) \left(\sqrt{x + 3} + 2\right)}$
${\lim}_{x \to 1} \frac{\cancel{\left(x - 1\right)}}{\cancel{\left(x - 1\right)} \left(\sqrt{x + 3} + 2\right)}$
as $x \to 1$ we get:
${\lim}_{x \to 1} \frac{1}{\left(\sqrt{x + 3} + 2\right)} = \frac{1}{4}$