# What is the limit of f(x)=0?

Given the function $f \left(x\right) = 0$, since this is a constant function (that is, for any value of $x$, $f \left(x\right) = 0$, the limit of the function as $x \to a$, where $a$ is any real number, is equal to $0$.
More specifically, as a constant function, $f \left(x\right)$ maintains the same value for any $x$. $f \left(1\right) = f \left(2\right) = f \left(\pi\right) = f \left(e\right) = f \left(- \frac{1258567}{44}\right) = 0$. Further, as a constant function, $f \left(x\right)$ is by definition continuous throughout its domain. Note, however, that if one arrives at a constant function via division or multiplication of non-constant functions (for example, $\frac{8 x}{x}$, there will still exist a discontinuity where the original denominator was $0$).
Graphing the function will further prove this point. On the graph $f \left(x\right) = 0$, the curve is simply the $x$-axis, which maintains a constant $y$-value of $0$ no matter the $x$-value.