Question

How to prove that the limit (as x goes to infinity) of a function's inverse (1/f(x)) cannot be zero, if the function's (f(x)) limit is zero?

Answer 1

assume that the function f is something trivial like\[1/x^{2}\]

then what about the inverse? it becomes nothing more than \[x^{2}\]

what is the limit then of the inverse? \[\infty\]