1 Answer

Jezabel · Answer 1 · 2018-06-24T20:22:14+0000

First of all, you have to understand

is a square-root function.

Square-root functions are continuous across their entire domain, and their domain is all real x-values for which the expression within the square-root is non-negative.

In other words, for any square-root function

and any input

in the domain of

(except for its endpoint), we know that this equality holds:
$lim \ q(x)=q(c)$

Let's take
√(x)

as an example.

The domain of
$\sqrt x$ is all real numbers such that
$x \geq 0$ . Since
x=0

is the endpoint of the domain, the two-sided limit at that point doesn't exist (you can't approach

from the left).

However, continuity at an endpoint only demands that the one-sided limit is equal to the function's value:

$lim \ √(x) = √(0) =0$

In conclusion, the equality
$lim \ q(x)=q(c)$ holds for any square-root function

and any real number

in the domain of

except for its endpoint, where the two-sided limit should be replaced with a one-sided limit.

The input
x=-3