Answer
$$1$$
Work Step by Step
Our aim is to compute the value of $\lim\limits_{t \to \infty} \dfrac{1+2^{-3t}}{1+5.3e^{-t}}$.
Here, we need to use the formula of:
$\lim \limits_{x\to a}f(x)=f(a)$, this implies that:
$\lim\limits_{t \to \infty} \dfrac{1+2^{-3t}}{1+5.3e^{-t}}=\dfrac{1+2^{-3(\infty)}}{1+5.3e^{-\infty}} \\=\dfrac{1+0}{1+0}\\=1$
