For a function f defined in some open interval containing a (but not necessarily at a itself), we say ,

lim as x approachs a f(x)=infinity,

if given any number M > 0, there is another number delta> 0 , such that 0 < | x - a | < delta guarantees that f (x) > M.

1. Prove that the following limit is correct by using the above mentioned definition.

lim as x approaches 0 (5/x^2=infinity)