Q:

Is $\lim _{ x\to \infty }\:x\:=\:\lim _{ t\to 0}\frac{1}{t}$?

Is $\lim _{ x\to \infty }\:x\:=\:\lim _{ t\to 0}\frac{1}{t}$  ?

A:

Both the limit are not defined, therefore we cannot say that they are equal (Since both tend to infinity, and two infinities need not to be equal), By the way if the limit is finite ;
$$\lim_{x \to \infty} f(x) = a=\lim_{t \to 0^{\color{red}+}} f\Big(\frac{1}{t}\Big)  $$
And ; 
$$\lim_{x \to ~-\infty} f(x) = a = \lim_{t \to 0^{\color{red}-}} f\Big(\frac{1}{t}\Big)  $$
Where , $a \in \mathbb{R}$

