I have this function which approaches zero in discrete steps:
$\frac{1}{2^{int(x)}}$
My question is that although this function shows asymptotic behaviour in that it approaches $y=0$ does it still have an asymptote even though it isn't continuous?
I have this function which approaches zero in discrete steps:
$\frac{1}{2^{int(x)}}$
My question is that although this function shows asymptotic behaviour in that it approaches $y=0$ does it still have an asymptote even though it isn't continuous?
One usually says that a function $f:(a,\infty)\to\mathbb R$ has horizontal asymptote $y=c$ if $\lim_{x\to \infty} f(x)=c \tag1$ The function $f(x)=2^{-\lfloor x\rfloor }$ satisfies (1) with $c=0$ and therefore has horizontal asymptote $y=0$.