 is to say that for every \(\epsilon\), there is an \(N\), such that whenever \(x&gt;N\), \(f(x)\) is within \(\epsilon\) of \(l\). For example, \(\lim_{x\to+\infty}e^{-x}=0\), because \(e^{-x}\) can be made as small as one likes by choosing large enough \(x\). (Note that the inputs to a function can be positive or negative, so we need to specify that \(x\) approaches positive infinity to distinguish this from the limit at the other end of the axis.)