## anonymous 5 years ago 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?

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? $\infty$