# How do you prove that the function 1/x is continuous at x=1?

Sep 27, 2016

See the Explanation.

#### Explanation:

To prove that a fun. $F \left(x\right)$ is continuous (cont.) at

$x = a , a \in {D}_{F} \text{=the Domain of } F$, we have to prove that,

${\lim}_{x \rightarrow a} F \left(x\right) = F \left(a\right)$.

So, in our case, we have,

${\lim}_{x \rightarrow 1} f \left(x\right)$

$= {\lim}_{x \rightarrow 1} \frac{1}{x}$

$= \frac{1}{1} = 1$.

$f \left(1\right) = 1$.

Thus, ${\lim}_{x \rightarrow 1} f \left(x\right) = f \left(1\right)$.

Hence, $f$ is cont. at $x = 1$.